## Regression Analysis and Its Techniques in Data Science

As a Data Science enthusiast, you might already know that a majority of business decisions these days are data-driven. However, it is essential to understand how to parse through all the data. One of the most important types of data analysis in this field is Regression Analysis. Regression Analysis is a form of predictive modeling technique mainly used in statistics. The term “regression” in this context, was first coined by Sir Francis Galton, a cousin of Sir Charles Darwin. The earliest form of regression was developed by Adrien-Marie Legendre and Carl Gauss - a method of least squares. Before getting into the what and how of regression analysis, let us first understand why regression analysis is essential. Why is regression analysis important? The evaluation of relationship between two or more variables is called Regression Analysis. It is a statistical technique.  Regression Analysis helps enterprises to understand what their data points represent, and use them wisely in coordination with different business analytical techniques in order to make better decisions. Regression Analysis helps an individual to understand how the typical value of the dependent variable changes when one of the independent variables is varied, while the other independent variables remain unchanged.  Therefore, this powerful statistical tool is used by Business Analysts and other data professionals for removing the unwanted variables and choosing only the important ones. The benefit of regression analysis is that it allows data crunching to help businesses make better decisions. A greater understanding of the variables can impact the success of a business in the coming weeks, months, and years in the future.  Data Science The regression method of forecasting, as the name implies, is used for forecasting and for finding the casual relationship between variables. From a business point of view, the regression method of forecasting can be helpful for an individual working with data in the following ways: Predicting sales in the near and long term. Understanding demand and supply. Understanding inventory levels. Review and understand how variables impact all these factors. However, businesses can use regression methods to understand the following: Why did the customer service calls drop in the past months? How the sales will look like in the next six months? Which ‘marketing promotion’ method to choose? Whether to expand the business or to create and market a new product. The ultimate benefit of regression analysis is to determine which independent variables have the most effect on a dependent variable. It also helps to determine which factors can be ignored and those that should be emphasized. Let us now understand what regression analysis is and its associated variables. What is regression analysis?According to the renowned American mathematician John Tukey, “An approximate answer to the right problem is worth a good deal more than an exact answer to an approximate problem". This is precisely what regression analysis strives to achieve.  Regression analysis is basically a set of statistical processes which investigates the relationship between a dependent (or target) variable and an independent (or predictor) variable. It helps assess the strength of the relationship between the variables and can also model the future relationship between the variables. Regression analysis is widely used for prediction and forecasting, which overlaps with Machine Learning. On the other hand, it is also used for time series modeling and finding causal effect relationships between variables. For example, the relationship between rash driving and the number of road accidents by a driver can be best analyzed using regression.  Let us now understand regression with an example. Meaning of RegressionLet us understand the concept of regression with an example. Consider a situation where you conduct a case study on several college students. We will understand if students with high CGPA also get a high GRE score. Our first job is to collect the details of the GRE scores and CGPAs of all the students of a college in a tabular form. The GRE scores and the CGPAs are listed in the 1st and 2nd columns, respectively. To understand the relationship between CGPA and GRE score, we need to draw a scatter plot.  Here, we can see a linear relationship between CGPA and GRE score in the scatter plot. This indicates that if the CGPA increases, the GRE scores also increase. Thus, it would also mean that a student with a high CGPA is likely to have a greater chance of getting a high GRE score. However, if a question arises like “If the CGPA of a student is 8.51, what will be the GRE score of the student?”. We need to find the relationship between these two variables to answer this question. This is the place where Regression plays its role. In a regression algorithm, we usually have one dependent variable and one or more than one independent variable where we try to regress the dependent variable "Y" (in this case, GRE score) using the independent variable "X" (in this case, CGPA). In layman's terms, we are trying to understand how the value of "Y" changes concerning the change in "X". Let us now understand the concept of dependent and independent variables. Dependent and Independent variables In data science, variables refer to the properties or characteristics of certain events or objects. There are mainly two types of variables while performing regression analysis which is as follows: Independent variables – These variables are manipulated or are altered by researchers whose effects are later measured and compared. They are also referred to as predictor variables. They are called predictor variables because they predict or forecast the values of dependent variables in a regression model. Dependent variables – These variables are the type of variable that measures the effect of the independent variables on the testing units. It is safer to say that dependent variables are completely dependent on them. They are also referred to as predicted variables. They are called because these are the predicted or assumed values by the independent or predictor variables. When an individual is looking for a relationship between two variables, he is trying to determine what factors make the dependent variable change. For example, consider a scenario where a student's score is a dependent variable. It could depend on many independent factors like the amount of study he did, how much sleep he had the night before the test, or even how hungry he was during the test.  In data models, independent variables can have different names such as “regressors”, “explanatory variable”, “input variable”, “controlled variable”, etc. On the other hand, dependent variables are called “regressand,” “response variable”, “measured variable,” “observed variable,” “responding variable,” “explained variable,” “outcome variable,” “experimental variable,” or “output variable.” Below are a few examples to understand the usage and significance of dependent and independent variables in a wider sense: Suppose you want to estimate the cost of living of a person using a regression model. In that case, you need to take independent variables as factors such as salary, age, marital status, etc. The cost of living of a person is highly dependent on these factors. Thus, it is designated as the dependent variable. Another scenario is in the case of a student's poor performance in an examination. The independent variable could be factors, for example, poor memory, inattentiveness in class, irregular attendance, etc. Since these factors will affect the student's score, the dependent variable, in this case, is the student's score.  Suppose you want to measure the effect of different quantities of nutrient intake on the growth of a newborn child. In that case, you need to consider the amount of nutrient intake as the independent variable. In contrast, the dependent variable will be the growth of the child, which can be calculated by factors such as height, weight, etc. Let us now understand the concept of a regression line. What is the difference between Regression and Classification?Regression and Classification both come under supervised learning methods, which indicate that they use labelled training datasets to train their models and make future predictions. Thus, these two methods are often classified under the same column in machine learning.However, the key difference between them is the output variable. In regression, the output tends to be numerical or continuous, whereas, in classification, the output is categorical or discrete in nature.  Regression and Classification have certain different ways to evaluate the predictions, which are as follows: Regression predictions can be interpreted using root mean squared error, whereas classification predictions cannot.  Classification predictions can be evaluated using accuracy, whereas, on the other hand, regression predictions cannot be evaluated using the same. Conclusively, we can use algorithms like decision trees and neural networks for regression and classification with small alterations. However, some other algorithms are more difficult to implement for both problem types, for example, linear regression for regressive predictive modeling and logistic regression for classification predictive modeling. What is a Regression Line?In the field of statistics, a regression line is a line that best describes the behaviour of a dataset, such that the overall distance from the line to the points (variable values) plotted on a graph is the smallest. In layman's words, it is a line that best fits the trend of a given set of data.  Regression lines are mainly used for forecasting procedures. The significance of the line is that it describes the interrelation of a dependent variable “Y” with one or more independent variables “X”. It is used to minimize the squared deviations of predictions.  If we take two variables, X and Y, there will be two regression lines: Regression line of Y on X: This gives the most probable Y values from the given values of X. Regression line of X on Y: This gives the most probable values of X from the given values of Y. The correlation between the variables X and Y depend on the distance between the two regression lines. The degree of correlation is higher if the regression lines are nearer to each other. In contrast, the degree of correlation will be lesser if the regression lines are farther from each other.  If the two regression lines coincide, i.e. only a single line exists, correlation tends to be either perfect positive or perfect negative. However, if the variables are independent, then the correlation is zero, and the lines of regression will be at right angles.  Regression lines are widely used in the financial sector and business procedures. Financial Analysts use linear regression techniques to predict prices of stocks, commodities and perform valuations, whereas businesses employ regressions for forecasting sales, inventories, and many other variables essential for business strategy and planning. What is the Regression Equation? In statistics, the Regression Equation is the algebraic expression of the regression lines. In simple terms, it is used to predict the values of the dependent variables from the given values of independent variables.  Let us consider one regression line, say Y on X and another line, say X on Y, then there will be one regression equation for each regression line: Regression Equation of Y on X: This equation depicts the variations in the dependent variable Y from the given changes in the independent variable X. The expression is as follows: Ye = a + bX Where,  Ye is the dependent variable, X is the independent variable, a and b are the two unknown constants that determine the position of the line. The parameter “a” indicates the distance of a line above or below the origin, i.e. the level of the fitted line, whereas parameter "b" indicates the change in the value of the independent variable Y for one unit of change in the dependent variable X. The parameters "a" and "b" can be calculated using the least square method. According to this method, the line needs to be drawn to connect all the plotted points. In mathematical terms, the sum of the squares of the vertical deviations of observed Y from the calculated values of Y is the least. In other words, the best-fitted line is obtained when ∑ (Y-Ye)2 is the minimum. To calculate the values of parameters “a” and “b”, we need to simultaneously solve the following algebraic equations: ∑ Y = Na + b ∑ X ∑ XY = a ∑ X + b ∑ X2 Regression Equation of X on Y: This equation depicts the variations in the independent variable Y from the given changes in the dependent variable X. The expression is as follows: Xe = a + bY  Where,  Xe is the dependent variable, Y is the independent variable, a and b are the two unknown constants that determine the position of the line. Again, in this equation, the parameter “a” indicates the distance of a line above or below the origin, i.e. the level of the fitted line, whereas parameter "b" indicates the slope, i.e. change in the value of the dependent variable X for a unit of change in the independent variable Y. To calculate the values of parameters “a” and “b” in this equation, we need to simultaneously solve the following two normal equations: ∑ X = Na + b ∑ Y ∑ XY = a ∑ Y + b ∑ Y2 Please note that the regression lines can be completely determined only if we obtain the constant values “a” and “b”. How does Linear Regression work?Linear Regression is a Machine Learning algorithm that allows an individual to map numeric inputs to numeric outputs, fitting a line into the data points. It is an approach to modeling the relationship between one or more variables. This allows the model to able to predict outputs. Let us understand the working of a Linear Regression model using an example. Consider a scenario where a group of tech enthusiasts has created a start-up named Orange Inc. Now, Orange has been booming since 2016. On the other hand, you are a wealthy investor, and you want to know whether you should invest your money in Orange in the next year or not. Let us assume that you do not want to risk a lot of money, so you buy a few shares. Firstly, you study the stock prices of Orange since 2016, and you see the following figure: It is indicative that Orange is growing at an amazing rate where their stock price has gone from 100 dollars to 500 dollars in only three years. Since you want your investment to boom along with the company's growth, you want to invest in Orange in the year 2021. You assume that the stock price will fall somewhere around $500 since the trend will likely not go through a sudden change. Based on the information available on the stock prices of the last couple of years, you were able to predict what the stock price is going to be like in 2021. You just inferred your model in your head to predict the value of Y for a value of X that is not even in your knowledge. This mental method you undertook is not accurate anyway because you were not able to specify what exactly will be the stock price in the year 2021. You just have an idea that it will probably be above 500 dollars. This is where Regression plays its role. The task of Regression is to find the line that best fits the data points on the plot so that we can calculate where the stock price is likely to be in the year 2021. Let us examine the Regression line (in red) by understanding its significance. By making some alterations, we obtained that the stock price of Orange is likely to be a little higher than 600 dollars by the year 2021. This example is quite oversimplified, so let us examine the process and how we got the red line on the next plot. Training the Regressor The example mentioned above is an example of Univariate Linear Regression since we are trying to understand the change in an independent variable X to one dependent variable, Y. Any regression line on a plot is based on the formula: f(X) = MX + B Where, M is the slope of the line, B is the y-intercept that allows the vertical movement of the line, And X is the function’s input variable. In the field of Machine Learning, the formula is as follows: h(X) = W0 + W1X Where, W0 and W1 are the weights, X is the input variable, h(X) is the label or the output variable. Regression works by finding the weights W0 and W1 that lead to the best-fitting line for the input variable X. The best-fitted line is obtained in terms of the lowest cost. Now, let us understand what does cost means here. The cost functionDepending upon the Machine Learning application, the cost could take different forms. However, in a generalized view, cost mainly refers to the loss or error that the regression model yields in its distance from the original training dataset. In a Regression model, the cost function is the Squared Error Cost: J(W0,W1) = (1/2n) Σ { (h(Xi) - Ti)2} for all i =1 until i = n Where, J(W0, W1) is the total cost of the model with weights W0 and W1, h(Xi) is the model’s prediction of the independent variable Y at feature X with index i, Ti is the actual y-value at index i, and n refers to the total number of data points in the dataset. The cost function is used to obtain the distance between the y-value the model predicted and the actual y-value in the data set. Then, the function squares this distance and divides it by the number of data points, resulting in the average cost. The 2 in the term ‘(1/2n)’ is merely to make the differentiation process in the cost function easier. Training the dataset Training a regression model uses a Learning Algorithm to find the weights W0 and W1 that will minimize the cost and plug them into the straight-line function to obtain the best-fitted line. The pseudo-code for the algorithm is as follows: Repeat until convergence { temp0 := W0 - a.((d/dW0) J(W0,W1)) temp1 := W1 - a.((d/dW1) J(W0,W1)) W0 = temp0 W1 = temp1 } Here, (d/dW0) and (d/dW1) refer to the partial derivatives of J(W0,, W1) concerning W0, and W1 respectively. The gist of the partial differentiation is basically the derivatives: (d/dW0) J(W0,W1) = W0 + W1.X - T (d/dW1) j(W0,W1) = (W0 + W1.X - T).X Implementing the Gradient Descent Learning algorithm will result in a model with minimum cost. The weights that led to the minimum cost are dealt with as the final values for the line function h(X) = W0 + W1X. Goodness-of-Fit in a Regression Model The Regression Analysis is a part of the linear regression technique. It examines an equation that lessens the distance between the fitted line and all data points. Determining how well the model fits the data is crucial in a linear model. The general idea is that if the deviations between the observed values and the predicted values of the linear model are small and unbiased, the model has well-fit data. In technical terms, “Goodness-of-fit” is a mathematical model describing the differences between the observed and expected values or how well the model fits a set of observations. This measure can be used in statistical hypothesis testing.How do businesses use Regression Analysis? Regression Analysis is a statistical technique used to evaluate the relationship between two or more independent variables. Organizations use regression analysis to understand the significance of their data points and use analytical techniques to make better decisions.Business Analysts and Data Professionals use this statistical tool to delete unwanted variables and select the significant ones. There are numerous ways that businesses use regression analysis. Let us discuss some of them below. 1. Decision-makingBusinesses need to make better decisions to run smoothly and efficiently, and it is also necessary to understand the effects of the decision taken. They collect data on various factors such as sales, investments, expenditures, etc. and analyze them for further improvements. Organizations use the Regression Analysis method by making sense of the data and gathering meaningful insights. Business analysts and data professionals use this method to make strategic business decisions.2. Optimization of business The main role of regression analysis is to convert the collected data into actionable insights. The old-school techniques like guesswork and assuming a hypothesis have been eliminated by organizations. They are now focusing on adopting data-driven decision-making techniques, which improves the work performance in an organization. This analysis helps the management sectors in an organization to take practical and smart decisions. The huge volume of data can be interpreted and understood to gain efficient insights. 3. Predictive Analysis Businesses make use of regression analysis to find patterns and trends. Business Analysts build predictions about future trends using historical data. Regression methods can also go beyond predicting the impact on immediate revenue. Using this method, you can forecast the number of customers willing to buy a service and use that data to estimate the workforce needed to run that service. Most insurance companies use regression analysis to calculate the credit health of their policyholders and the probable number of claims in a certain period. Predictive Analysis helps businesses to: Minimize costs Minimize the number of required tools Provide fast and efficient results Detect fraud Risk Management Optimize marketing campaigns 4. Correcting errors Regression Analysis is not only used for predicting trends, but it is also useful to identify errors in judgements. Let us consider a situation where the executive of an organization wants to increase the working hours of its employees and make them work extra time to increase the profits. In such a case, regression analysis analyses all the variables and it may conclude that an increase in the working hours beyond their existing time of work will also lead to an increase in the operation expense like utilities, accounting expenditures, etc., thus leading to an overall decrease in the profit. Regression Analysis provides quantitative support for better decision-making and helps organizations minimize mistakes. 5. New Insights Organizations generate a large amount of cluttered data that can provide valuable insights. However, this vast data is useless without proper analysis. Regression analysis is responsible for finding a relationship between variables by discovering patterns not considered in the model. For example, analyzing data from sales systems and purchase accounts will result in market patterns such as increased demand on certain days of the week or at certain times of the year. You can maintain optimal stock and personnel using the information before a demand spike arises. The guesswork gets eliminated by data-driven decisions. It allows companies to improve their business performance by concentrating on the significant areas with the highest impact on operations and revenue. Use cases of Regression AnalysisPharmaceutical companies Pharmaceutical organizations use regression analysis to analyze the quantitative stability data for the retest period or estimate shelf life. In this method, we find the nature of the relationship between an attribute and time. We determine whether the data should be transformed for linear regression analysis or non-linear regression analysis using the analyzed data. FinanceThe simple linear regression technique is also called the Ordinary Least Squares or OLS method. This method provides a general explanation for placing the line of the best fit among the data points. This particular tool is used for forecasting and financial analysis. You can also use it with the Capital Asset Pricing Model (CAPM), which depicts the relationship between the risk of investing and the expected return. Credit Card Credit card companies use regression analysis to analyze various factors such as customer's risk of credit default, prediction of credit balance, expected consumer behaviour, and so on. With the help of the analyzed information, the companies apply specific EMI options and minimize the default among risky customers. When Should I Use Regression Analysis? Regression Analysis is mainly used to describe the relationships between a set of independent variables and the dependent variables. It generates a regression equation where the coefficients correspond to the relationship between each independent and dependent variable. Analyze a wide variety of relationships You can use the method of regression analysis to perform many things, for example: To model multiple independent variables. Include continuous and categorical variables. Use polynomial terms for curve fitting. Evaluate interaction terms to examine whether the effect of one independent variable is dependent on the value of another variable. Regression Analysis can untangle very critical problems where the variables are entwined. Consider yourself to be a researcher studying any of the following: What impact does socio-economic status and race have on educational achievement? Do education and IQ affect earnings? Impact of exercise habits and diet affect weight. Do drinking coffee and smoking cigarettes reduce the mortality rate? Does a particular exercise have an impact on bone density? These research questions create a huge amount of data that entwines numerous independent and dependent variables and question their influence on each other. It is an important task to untangle this web of related variables and find out which variables are statistically essential and the role of each of these variables. To answer all these questions and rescue us in this game of variables, we need to take the help of regression analysis for all the scenarios. Control the independent variables Regression analysis describes how the changes in each independent variable are related to the changes in the dependent variable and how it is responsible for controlling every variable in a regression model. In the process of regression analysis, it is crucial to isolate the role of each variable. Consider a scenario where you participated in an exercise intervention study. You aimed to determine whether the intervention was responsible for increasing the subject's bone mineral density. To achieve an outcome, you need to isolate the role of exercise intervention from other factors that can impact the bone density, which can be the diet you take or any other physical activity. To perform this task, you need to reduce the effect of the unsupportive variables. Regression analysis estimates the effect the change in one dependent variable has on the dependent variables while all other independent variables are constant. This particular process allows you to understand each independent variable's role without considering the other variables in the regression model. Now, let us understand how regression can help control the other variables in the process. According to a recent study on the effect of coffee consumption on mortality, the initial results depicted that the higher the intake of coffee, the higher is the risk of death. However, researchers did not include the fact that most coffee drinkers smoke in their first model. After smoking was included in the model, the regression results were quite different from the initial results. It depicted that coffee intake lowers the risk of mortality while smoking increases it. This model isolates the role of each variable while holding the other variables constant. You can examine the effect of coffee intake while controlling the smoking factor. On the other hand, you can also look at smoking while controlling for coffee intake. This particular example shows how omitting a significant variable can produce misleading results and causes it to be uncontrolled. This warning is mainly applicable for observational studies where the effects of omitted significant variables can be unbalanced. This omitted variable bias can be minimized in a randomization process where true experiments tend to shell out the effects of these variables in an equal manner. What are Residuals in Regression Analysis? Residuals identify the deviation of observed values from the expected values. They are also referred to as error or noise terms. It gives an insight into how good our model is against the actual value, but there are no real-life representations of residual values. Calculating the real values of intercept, slope, and residual terms can be a complicated task. However, the Ordinary Least Square (OLS) regression technique can help us speculate on an efficient model. The technique minimizes the sum of the squared residuals. With the help of the residual plots, you can check whether the observed error is consistent with stochastic error (differences between the expected and observed values must be random and unpredictable). What are the Linear model assumptions in Regression Analysis? Regression Analysis is the first step in the process of predictive modeling. It is quite easy to implement, and its syntax and parameters do not create any kind of confusion. However, the purpose of regression analysis is not just solved by running a single line of code. It is much more than that. The function plot(model_name) returns four plots in the R programming language. Each of these plots provides essential information about the dataset. Most beginners in the field are unable to trace the information. But once you understand these plots, you can bring important improvements to your regression model. For significant improvements in your regression model, it is also crucial to understand the assumptions you need to take in your model and how you can fix them if any assumption gets violated. The four assumptions that should be met before conducting linear regression are as follows: Linear Relationship: A linear relationship exists between the independent variable, x, and the dependent variable, y. Independence: The residuals in linear regression are independent. In other words, there is no correlation between consecutive residuals in time series data. Homoscedasticity: Residuals have constant variance at every level of X. Normality: The residuals of the model are normally distributed. Assumption 1: Linear Relationships Explanation The first assumption in Linear regression is that there is a linear relationship between the independent variable X and the dependent variable Y. How to determine if this assumption is met The quickest and easiest way to detect this assumption is by creating a scatter plot of X vs Y. By looking at the scatter plot, you can have a visual representation of the linear relationship between the two variables. If the points in the plot could fall along a straight line, then there exists some type of linear relationship between the variables, and this assumption is met. For example, consider this first plot below. The points in the plot look like they fall roughly on a straight line, which indicates that there exists a linear relationship between X and Y: However, there doesn’t appear to be a linear relationship between X and Y in this second plot below: And in this third plot, there appears to be a clear relationship between X and Y, but a linear relationship between:What to do if this assumption is violated If you create a scatter plot between X and Y and do not find any linear relationship between the two variables, then you can do two things: You can apply a non-linear transformation to the dependent or independent variables. Common examples might include taking the log, the square root, or the reciprocal of the independent and dependent variable. You can add another independent variable to the regression model. If the plot of X vs Y has a parabolic shape, then adding X2 as an additional independent variable in the linear regression model might make sense. Assumption 2: Independence Explanation The second assumption of linear regression is that the residuals should be independent. Its relevance can be seen while working with time-series data. In an ideal manner, a pattern among consecutive residuals is not what we want. For example, in a time series model, the residuals should not grow steadily along with time. How to determine if this assumption is met To determine if this assumption is met, we need to have a scatter plot of residuals vs time and look at the residual time series plot. In an ideal plot, the residual autocorrelations should fall within the 95% confidence bands around zero, located at about +/- 2-over the square root on n, where n denotes the sample size. You can also perform the Durbin-Watson test to formally examine if this assumption is met. What to do if this assumption is violated If this assumption is violated, you can do three things which are as follows: If there is a positive serial correlation, you can add lags of the independent variable or dependent variable to the regression model. If there is a negative serial correlation, check that none of the variables has differences. If there is a seasonal correlation, consider adding a seasonal dummy variable into your regression model. Assumption 3: HomoscedasticityExplanation The third assumption of linear regression is that the residuals should have constant variance at every level of X. This property is called homoscedasticity. When homoscedasticity is not present, the residuals suffer from heteroscedasticity. The outcome of the regression analysis becomes hard to trust when heteroscedasticity is present in the model. It increases the variance of the regression coefficient estimates, but the model does not recognize this fact. This makes the model declare that a term in the model is significantly crucial, but it is not. How to determine if this assumption is met To determine if this assumption is met, we need to have a scatter plot of fitted values vs residual plots. To achieve this, you need to fit a regression line into a data set. Below is a scatterplot showing a typical fitted value vs residual plot in which heteroscedasticity is present: You can observe how the residuals become much more spread out as the fitted values get larger. The “cone” shape is a classic sign of heteroscedasticity: What to do if this assumption is violated If this assumption is violated, you can do three things which are as follows: Transform the dependent variable: The most common transformation is simply taking the dependent variable's log. Consider if you are using population size as an independent variable to predict the number of flower shops in a city as the dependent variable. You need to use population size to predict the number of flower shops in a city. It causes heteroscedasticity to go away. Redefine the dependent variable: One common way is to use a rate rather than the raw value. Consider the previous example. In that case, use population size to predict the number of flower shops per capita instead. This reduces the variability that naturally occurs among larger populations. Use weighted regression: The third way to fix heteroscedasticity is to use weighted regression. In this regression method, we assign a weight to each data point depending on the variance of its fitted value, giving small weights to data points having higher variances, which shrinks their squared residuals. When the proper weights are used, the problem of heteroscedasticity gets eradicated. Assumption 4: Normality Explanation We need to take the last assumption that the residuals should be normally distributed. How to determine if this assumption is met To determine if this assumption is met, there are two common ways to achieve that: 1. Use Q-Q plots to examine the assumption visually. Also known as the quantile-quantile plot, it is used to determine whether or not the residuals of the regression model follow a normal distribution. The normality assumption is achieved if the points on the plot roughly form a straight diagonal line as follows: However, this Q-Q plot below shows when the residuals clearly deviate from a straight diagonal line, they do not follow a normal distribution: 2. Some other formal statistical tests to check the normality assumption are Shapiro-Wilk, Kolmogorov-Smirnov, Jarque-Barre, and D'Agostino-Pearson. These tests however have a limitation as they are used only when there are large sample sizes and it often results that the residuals are not normal. Therefore, graphical techniques like Q-Q plots are easier to check the normality assumption and are also more preferable. What to do if this assumption is violatedIf this assumption is violated, you can do two things which are as follows: Firstly, examine if outliers are present and exist, make sure they are real values and aren’t data errors. Also, verify that any outliers aren’t having a large impact on the distribution. Secondly, you can apply a non-linear transformation to the independent and/or dependent variables. Common examples include taking the log, the square root, or the reciprocal of the independent and/or dependent variable. How to perform a simple linear regression?The formula for a simple linear regression is: Y = B0 + B1X + e Where, Y refers to the predicted value of the dependent variable Y for any given value of the independent variable X. B0 denotes the intercept, i.e. the predicted value of y when the x is 0. B1 denotes the regression coefficient, i.e. how much we expect the value of y to change as the value of x increases. X refers to the independent variable, or the variable we expect is influencing y). e denotes the error estimate, i.e. how much variation exists in our regression coefficient estimate. The Linear regression model's task is to find the best-fitted line through the data by looking out for the regression coefficient B1 that minimizes the total error estimate e of the model. Simple linear regression in R R is a free statistical programming language that most data professionals use very powerful and widely. Let us consider a dataset of income and happiness that we will use to perform regression analysis.The first task is to load the income.data dataset into the R environment, and then generate a linear model describing the relationship between income and happiness by the command as follows: income.happiness.lm <- lm(happiness ~ income, data = income.data) The code above mentioned takes the data that has been collected using data = income.data. Then, it estimates the impact of the independent variable income on the dependent variable happiness using the linear model equation: lm() Interpreting the resultsTo obtain and visualize the results of the simple linear regression model, you can use the summary() function in R by executing the following code: summary(income.happiness.lm) What this function does is it takes the essential factors from the linear model and puts them into a tabular form, which looks like this: According to the output table, the first thing it does is repeat the formula used to generate the results (‘Call’). The next thing it does is summarize the model residuals (‘Residuals’), which explains how well the model fits the real data. Next, you can see the ‘Coefficients’ table. The first row of this table provides the estimates of the y-intercept, and the second row provides the regression coefficient of the model.The first row of the ‘Coefficients’ table is labelled (Intercept), the Y-intercept of the regression equation, with a value of 0.20. Now, if you want to predict the happiness values across the range of observed values of income, you need to insert this into your regression equation : happiness = 0.20 + 0.71*income ± 0.018 The next row in the ‘Coefficients’ table is income that describes the estimated effect of income on reported happiness. The Estimate column is the estimated effect or the regression coefficient (R2) value. The table (0.713) indicates that for every unit increase in income, there is a corresponding 0.71-unit increase in reported happiness. The column of Std. Error displays the standard error of the estimate, which shows how much variation there is in the estimate of the relationship between income and happiness. The t value column displays the test statistic. The test statistic used in a linear regression model is the t-value from a two-sided t-test unless specified otherwise. The results depend on the test statistic. The larger the test statistic, the less probable that our results occurred by chance. The Pr(>| t |) column displays the p-value, which tells us how probable we are to see the estimated effect of income on happiness considering the null hypothesis of no effect were true. We can reject the null hypothesis since the p-value is very low (p < 0.001), and finally, we can conclude that income has a statistically crucial effect on happiness. The most important thing here in the linear regression model is the p-value. In this example, it is quite significant (p < 0.001), which shows that this model is a good fit for the observed data. Presenting the results While presenting your results, you should include the regression coefficient, standard error of the estimate, and the p-value. You should also interpret your numbers so that readers can have a clear understanding of the regression coefficient: A significant relationship (p < 0.001) has been found between income and happiness (R2 = 0.71 ± 0.018), with a 0.71-unit increase in reported happiness for every$10,000 increase in income. For a simple linear regression, you can simply plot the observations on the x and y-axis of a scatter plot and then include the regression line and regression function.What is multiple regression analysis?Multiple Regression is an extension of simple linear regression and is used to estimate the relationship between two or more independent variables and one dependent variable. You can perform multiple regression analysis to know: The strength of the relationship between one or more independent variables and one dependent variable. For example, you can use it to understand whether the exam performance can be predicted based on revision time, test anxiety, lecture attendance, and gender.  The overall fit, i.e. variance of the model and the relative impact of each of the predictors to the total variance explained. For example, you might want to know how much of the variation in the student’s exam performance can be understood by revision time, test anxiety, lecture attendance, gender, and the relative impact of each independent variable in explaining the variance. How to perform multiple linear regression? The formula for multiple linear regression is: Y = B0 + B1X1 + … + BnXn + e Where, Y refers to the predicted value of the dependent variable Y for any given value of the independent variable X. B0 denotes the intercept, i.e. the predicted value of y when the x is 0. B1X1  denotes the regression coefficient (B1), i.e. how much we expect the value of Y to change as the value of X increases. ... does the same for all the independent variables we want to test. BnXn refers to the regression coefficient of the last independent variable e denotes the error estimate of the model, i.e. how much variation exists in our estimate of the regression coefficient. It is the task of the Multiple Linear regression model to find the best-fitted line through the data by calculating the following three things: The regression coefficients will lead to the least error in the overall multiple regression model. The t-statistic of the overall regression model. The associated p-value  The multiple regression model also calculates the t-statistic and p-value for each regression coefficient. Multiple linear regression in R Let us consider a dataset of the heart and other factors that affect the functioning of our heart to perform multiple regression analyses. The first task is to load the heart.data dataset into the R environment, and then generate a linear model describing the relationship between heart disease and biking to work by the command as follows: heart.disease.lm<-lm(heart.disease ~ biking + smoking, data = heart.data) The code above mentioned takes the data that has been collected using data = heart.data. Then, it estimates the impact of the independent variable biking and smoking on the dependent variable heart disease using the linear model equation:  lm()  Interpreting the resultsTo obtain and visualize the results of the simple linear regression model, you can use the summary() function in R by executing the following code: summary(heart.disease.lm) What this function does is it takes the essential factors from the linear model and puts them into a tabular form, which looks like this:According to the output table, the first thing it does is repeat the formula used to generate the results (‘Call’). The next thing it does is summarize the model residuals (‘Residuals’), which explains how well the model fits the real data.  If the residuals are roughly centred around zero and with a similar spread on either side, then the model probably fits the assumption of heteroscedasticity. Next, you can see the ‘Coefficients’ table. The first row of this table provides the estimates of the y-intercept, and the second row provides the regression coefficient of the model. The first row of the ‘Coefficients’ table is labelled (Intercept), the Y-intercept of the regression equation. Now, if you want to predict the biking and smoking values across the range of observed values of heart, you need to insert this into your regression equation : heart disease = 15 + (-0.2*biking) + (0.178*smoking) ± eThe Estimate column is the estimated effect or the regression coefficient  (R2) value. The estimates in the table tell us that for every 1% increase in biking to work, there is an associated 0.2 % decrease in heart disease. For every 1% increase in smoking, there is an associated 0.17 % increase in heart disease. The column of Std. Error displays the standard error of the estimate, which shows how much variation there is in the estimate of the relationship between income and happiness. The t value column displays the test statistic. The test statistic used in a  linear regression model is the t-value from a two-sided t-test unless specified otherwise. The results depend on the test statistic. The larger the test statistic, the less probable that our results occurred by chance. The Pr(>| t |) column displays the p-value, which tells us how probable we are to see the estimated effect of income on happiness considering the null hypothesis of no effect were true. We can reject the null hypothesis since the p-value is very low (p < 0.001), and finally, we can conclude that both - biking to work and smoking - have influenced rates of heart disease. The most important thing here in the linear regression model is the p-value. In this example, it is quite significant (p < 0.001), which shows that this model is a good fit for the observed data. Presenting the results While presenting your results, you should include the regression coefficient, standard error of the estimate, and the p-value. You should also interpret your numbers in the proper context so that readers can have a clear understanding of the regression coefficient:  In our survey of 500 towns, we found significant relationships between the frequency of biking to work and the frequency of heart disease and the frequency of smoking and heart disease (p < 0.001 for each). Specifically, we found a 0.2% decrease (± 0.0014) in the frequency of heart disease for every 1% increase in biking and a 0.178% increase (± 0.0035) in the frequency of heart disease for every 1% increase in smoking. For multiple linear regression, you can simply plot the observations on the X and Y-axis of a scatter plot and then include the regression line and regression function: In this example, we have calculated the predicted values of the dependent variable heart disease across the observed values for the percentage of people biking to work. However, to include the effect of smoking on the independent variable heart disease, we had to calculate the predicted values by holding the variable smoking as constant at the minimum, mean, and maximum observed smoking rates. What is R-squared in Regression Analysis? In data science, R-squared (R2) is the coefficient of determination or the coefficient of multiple determination in case of multiple regression.  In the linear regression model, R-squared acts as an evaluation metric to evaluate the scatter of the data points around the fitted regression line. It recognizes the percentage of variation of the dependent variable. R-squared and the Goodness-of-fit R-squared is the proportion of variance in the dependent variable that the independent variable can explain.The value of R-squared stays between 0 and 100%: 0% corresponds to a model that does not explain the variability of the response data around its mean. The mean of the dependent variable helps predict the dependent variable and the regression model. On the other hand, 100% corresponds to a model that explains all the variability of the response variable around its mean. If your value of R2  is large, you have a better chance of your regression model fitting the observations.Although you get essential insights about the regression model in this statistical measure, you should not depend on it for the complete assessment of the model. It lacks information about the relationship between the dependent and the independent variables. It also does not inform about the quality of the regression model. Hence, as a user, you should always analyze R2 and other variables and then derive conclusions about the regression model. Visual Representation of R-squared You can visually demonstrate the plots of fitted values by observed values in a graphical manner. It illustrates how R-squared values represent the scatter around the regression line.  As observed in the pictures above, the value of R-squared for the regression model on the left side is 17%, and for the model on the right is 83%. When the variance accounts to be high in a regression model, the data points tend to fall closer to the fitted regression line.  However, a regression model with an R2 of 100% is an ideal scenario that is impossible. In such a case, the predicted values equal the observed values, leading all the data points to fall exactly on the regression line.  Interpretation of R-squared The simplest interpretation of R-squared is how good the regression model fits the observed data values. Let us loot at an example to understand this. Consider a model where the  R2  value is 70%. This would mean that the model explains 70% of the fitted data in the regression model. Usually, when the R2  value is high, it suggests a better fit for the model. The correctness of the statistical measure does not only depends on R2. Still, it can depend on other several factors like the nature of the variables, the units on which the variables are measured, etc. So, a high R-squared value is not always likely for the regression model and can indicate problems too.A low R-squared value is a negative indicator for a model in general. However, if we consider the other factors, a low R2 value can also result in a good predictive model. Calculation of R-squared R- squared can be evaluated using the following formula:  Where: SSregression – Explained sum of squares due to the regression model. SStotal – The total sum of squares. The sum of squares due to regression assesses how well the model represents the fitted data. The total sum of squares measures the variability in the data used in the regression model.Now let us come back to the earlier situation where we have two factors: the number of hours of study per day and the score in a particular exam to understand the calculation of R-squared more effectively. Here, the target variable is represented by score and the independent variable by the number of study hours per day.  In this case, we will need a simple linear regression model and the equation of the model will be as follows:  ŷ = w1x1 + b  The parameters w1 and b can be calculated by reducing the squared error over all the data points. The following equation is called the least square function:minimize ∑(yi –  w1x1i – b) Now, R-squared calculates the amount of variance of the target variable explained by the model, i.e. function of the independent variable. However, to achieve that, we need to calculate two things: Variance of the target variable: var(avg) = ∑(yi – Ӯ)2 The variance of the target variable around the best-fit line: var(model) = ∑(yi – ŷ)2Finally, we can calculate the equation of R-squared as follows:  R2 = 1 – [var(model)/var(avg)] = 1 -[∑(yi – ŷ)2/∑(yi – Ӯ)2]    What are the different types of regression analysis?   Other than simple linear regression and multiple linear regression, there are mainly 5 types of regression techniques. Let us discuss them one by one.  Polynomial RegressionIn a polynomial regression technique, the power of the independent variable has to more than 1. The expression below shows a polynomial equation: y = a + bx2  In this regression technique, the best-fitted line is a curve line instead of a straight line that fits into the data points. An important point to keep in mind while performing polynomial regression is, if you try to fit a polynomial of a higher degree to get a lower error, it might result in overfitting.  You should always plot the relationships to see the fit and always make sure that the curve fits the nature of the problem. An example to illustrate how plotting can help: Logistic Regression The logistic regression technique is used when the dependent variable is discrete in nature. For example, 0 or 1, true or false, etc. The target variable in this regression can have only two values and the relation between the target variable and the independent variable is denoted by a sigmoid curve. To measure the relationship between the target variable and independent variables,  Logit function is used. The expression below shows a logistic equation: logit(p) = ln(p/(1-p)) = b0 + b1X1 + b2X2 + b3X3 …. + bkXk Where,  p denotes the probability of occurrence of the feature. Ridge Regression The Ridge Regression technique is usually used when there is a high correlation between the independent variables. This is because the least square estimates result in unbiased values when there are multi collinear data.  However, if the collinearity is very high, there exists some bias value. Therefore, it is crucial to introduce a bias matrix in the equation of Ridge Regression. This regression method is quite powerful where the model is less susceptible to overfitting. The expression below shows a ridge regression equation: β = (X^{T}X + λ*I)^{-1}X^{T}y The lambda (λ) in the equation solves the issue of multicollinearity. Lasso Regression Lasso Regression is one of the types of regression in machine learning that is responsible for performing regularization and feature selection. It restricts the absolute size of the regression coefficient, due to which the coefficient value gets nearer to zero.The feature selection method in Lasso Regression allows the selection of a set of features from the dataset to build the model. Only the required features are used in this regression, while others are made zero. This helps in avoiding overfitting in the model.  If the independent variables are highly collinear, then this regression technique takes only one variable and makes other variables shrink to zero. The expression below shows a lasso regression equation: N^{-1}Σ^{N}_{i=1}f(x_{i}, y_{I}, α, β) Bayesian RegressionIn the Bayesian Regression method, the Bayes theorem is used to determine the value of regression coefficients. In this linear regression technique, the posterior distribution of the features is evaluated other than finding the least-squares.  Bayesian Linear Regression collaborates with Linear Regression and Ridge Regression but is more stable than simple Linear Regression. What are the terminologies used in Regression Analysis? When trying to understand the outcome of regression analysis, it is important to understand the key terminologies used to acknowledge the information.  A comprehensive list of regression analysis terms used are described below: Estimator: An estimator is an algorithm for generating estimates of parameters when the relevant dataset is present. Bias: An estimate is said to be unbiased when its expectation is the same as the value of the parameter that is being estimated. On the other hand, if the expectation is the same as the value of the estimated parameter, it is said to be biased. Consistency: An estimator is consistent if the estimates it produces converge on the value of the true parameter considering the sample size increases without limit. For example, an estimator that produces estimates θ^ for some value of parameter θ, where ^ is a small number. If the estimator is consistent, we can make the probability as close to 1.0 or as small as we like by drawing a sufficiently large sample.  Efficiency: An estimator “A” is said to be more efficient than an estimator “B” when “A” has a smaller sampling variance, i.e. if the specific values of “A” are more tightly clustered around their expectation. Standard error of the Regression (SER): It is defined as estimating the standard deviation of the error term in a regression model. Standard error of regression coefficient: It is defined as estimating the standard deviation of the sampling distribution for a particular coefficient term. P-value: P-value is the probability when the null hypothesis is considered true, of drawing sample data that are as adverse to the null as the data drawn, or more so. When the p-value is small, there are two possibilities for that – firstly, a low-probability unrepresentative sample is drawn, or secondly, the null hypothesis is false. Significance level: For a hypothesis test, the significance test is the smallest p-value for which the null hypothesis is not rejected. If the significance level is 1%, the null is rejected if and only if the p-value for the test is less than 0.01. The significance level can also be defined as the probability of making a type 1 error, i.e. rejecting a true null hypothesis. Multicollinearity: It is a situation where there is a high degree of correlation among the independent variables in a regression mod. In other words, a situation where some of the X values are close to being linear combinations of other X values. Multicollinearity occurs due to large standard errors and when the regression model cannot produce precise parameter estimates. This problem mainly occurs while estimating causal influences.T-test: The t-test is a common test for the null hypothesis that Bi's particular regression parameter has some specific value. F-test: F-test is a method for jointly testing a set of linear restrictions on a regression model. Omitted variable bias: Omitted variable bias is a bias in estimating regression parameters. It generally occurs when a relevant independent variable is omitted from a model, and the omitted variable is correlated with one or more of the included variables. Log variables: It is a transformation method that allows the estimation of a non-linear model using the OLS method to exchange the natural log of a variable for the level of that variable. It is performed for the dependent variable and/or one or more independent variables. Quadratic terms: This is another common transformation method where both xi and x2i are included as regressors. The estimated effect of xi on y is calculated by finding the derivative of the regression equation concerning xi.  Interaction terms: These are the pairwise products of the "original" independent variables. The interaction terms allow for the possibility that the degree to which xi affects y depends on the value of some other variable Xj. For example, the effect of experience on wages xi might depend on the gender xj of the worker. What are the tips to avoid common problems working with regression analysis? Regression is a very powerful statistical analysis that offers high flexibility but presents a variety of potential pitfalls. Let us see some tips to overcome the most common problems whilst working with regression analysis.Tip 1:  Research Before Starting Before you start working with regression analysis, review the literature to understand the relevant variables, the relationships they have, and the expected coefficient signs and effect magnitudes. It will help you collect the correct data and allow you to implement the best regression equation.  Tip 2: Always prefer Simple Models Start with a simple model and then make it more complicated only when needed. When you have several models with different predictive abilities, always prefer the simplest model because it will be more likely to be the best model. Another significant benefit of simpler models is that they are easier to understand and explain to others.  Tip 3: Correlation Does Not Imply Causation  Always remember correlation doesn't imply causation. Causation is a completely different thing as compared to causation. In general, to establish causation, you need to perform a designed experiment with randomization. However, If you’re using regression analysis to analyze the uncollected data in an experiment, causation is uncertain.Tip 4: Include Graphs, Confidence, and Prediction Intervals in the Results   The presentation of your results can influence the way people interpret them. For instance, confidence intervals and statistical significance provide consistent information.  According to a study, statistical reports that refer only to statistical significance only bring about correct interpretations 40% of the time. On the other hand, when the results also include confidence intervals, the percentage rises to 95%. Tip 5: Check the Residual Plots Residual plots are the quickest and easiest method to examine the problems in a regression model and allow you to make adjustments. For instance, residual plots help display patterns when you cannot model curvature present in your data. Regression Analysis and The Real World  Let us summarize what we have covered in this article so far: Regression Analysis and its importance. Difference between regression and classification. Regression Line and Regression Equation. How companies use regression analysis When to use regression analysis. Assumptions in Regression Analysis. Simple and Multiple linear regression. R-squared: Representation, Interpretation, Calculation. Types of Regression. Terminologies used in Regression. How to avoid problems in regression. Regression Analysis is an interesting machine learning technique utilized extensively by enterprises to transform data into useful information. It continues to be a significant asset to many leading sectors starting from finance, education, banking, retail, medicine, media, etc.

# Regression Analysis and Its Techniques in Data Science

6K

As a Data Science enthusiast, you might already know that a majority of business decisions these days are data-driven. However, it is essential to understand how to parse through all the data. One of the most important types of data analysis in this field is Regression Analysis.

Regression Analysis is a form of predictive modeling technique mainly used in statistics. The term “regression” in this context, was first coined by Sir Francis Galton, a cousin of Sir Charles Darwin. The earliest form of regression was developed by Adrien-Marie Legendre and Carl Gauss - a method of least squares.

Before getting into the what and how of regression analysis, let us first understand why regression analysis is essential.

## Why is regression analysis important?

The evaluation of relationship between two or more variables is called Regression Analysis. It is a statistical technique.

Regression Analysis helps enterprises to understand what their data points represent, and use them wisely in coordination with different business analytical techniques in order to make better decisions.

Regression Analysis helps an individual to understand how the typical value of the dependent variable changes when one of the independent variables is varied, while the other independent variables remain unchanged.  Therefore, this powerful statistical tool is used by Business Analysts and other data professionals for removing the unwanted variables and choosing only the important ones.

The benefit of regression analysis is that it allows data crunching to help businesses make better decisions. A greater understanding of the variables can impact the success of a business in the coming weeks, months, and years in the future.

Data Science

The regression method of forecasting, as the name implies, is used for forecasting and for finding the casual relationship between variables. From a business point of view, the regression method of forecasting can be helpful for an individual working with data in the following ways:

• Predicting sales in the near and long term.
• Understanding demand and supply.
• Understanding inventory levels.
• Review and understand how variables impact all these factors.

However, businesses can use regression methods to understand the following:

• Why did the customer service calls drop in the past months?
• How the sales will look like in the next six months?
• Which ‘marketing promotion’ method to choose?
• Whether to expand the business or to create and market a new product.

The ultimate benefit of regression analysis is to determine which independent variables have the most effect on a dependent variable. It also helps to determine which factors can be ignored and those that should be emphasized.

Let us now understand what regression analysis is and its associated variables.

## What is regression analysis?

According to the renowned American mathematician John Tukey, “An approximate answer to the right problem is worth a good deal more than an exact answer to an approximate problem". This is precisely what regression analysis strives to achieve.

Regression analysis is basically a set of statistical processes which investigates the relationship between a dependent (or target) variable and an independent (or predictor) variable. It helps assess the strength of the relationship between the variables and can also model the future relationship between the variables.

Regression analysis is widely used for prediction and forecasting, which overlaps with Machine Learning. On the other hand, it is also used for time series modeling and finding causal effect relationships between variables. For example, the relationship between rash driving and the number of road accidents by a driver can be best analyzed using regression.

Let us now understand regression with an example.

### Meaning of Regression

Let us understand the concept of regression with an example.

Consider a situation where you conduct a case study on several college students. We will understand if students with high CGPA also get a high GRE score.

Our first job is to collect the details of the GRE scores and CGPAs of all the students of a college in a tabular form. The GRE scores and the CGPAs are listed in the 1st and 2nd columns, respectively.

To understand the relationship between CGPA and GRE score, we need to draw a scatter plot.

Here, we can see a linear relationship between CGPA and GRE score in the scatter plot. This indicates that if the CGPA increases, the GRE scores also increase. Thus, it would also mean that a student with a high CGPA is likely to have a greater chance of getting a high GRE score.

However, if a question arises like “If the CGPA of a student is 8.51, what will be the GRE score of the student?”. We need to find the relationship between these two variables to answer this question. This is the place where Regression plays its role.

In a regression algorithm, we usually have one dependent variable and one or more than one independent variable where we try to regress the dependent variable "Y" (in this case, GRE score) using the independent variable "X" (in this case, CGPA). In layman's terms, we are trying to understand how the value of "Y" changes concerning the change in "X".

Let us now understand the concept of dependent and independent variables.

### Dependent and Independent variables

In data science, variables refer to the properties or characteristics of certain events or objects.

There are mainly two types of variables while performing regression analysis which is as follows:

• Independent variables – These variables are manipulated or are altered by researchers whose effects are later measured and compared. They are also referred to as predictor variables. They are called predictor variables because they predict or forecast the values of dependent variables in a regression model.
• Dependent variables  These variables are the type of variable that measures the effect of the independent variables on the testing units. It is safer to say that dependent variables are completely dependent on them. They are also referred to as predicted variables. They are called because these are the predicted or assumed values by the independent or predictor variables.

When an individual is looking for a relationship between two variables, he is trying to determine what factors make the dependent variable change. For example, consider a scenario where a student's score is a dependent variable. It could depend on many independent factors like the amount of study he did, how much sleep he had the night before the test, or even how hungry he was during the test.

In data models, independent variables can have different names such as “regressors”, “explanatory variable”, “input variable”, “controlled variable”, etc. On the other hand, dependent variables are called “regressand,” “response variable”, “measured variable,” “observed variable,” “responding variable,” “explained variable,” “outcome variable,” “experimental variable,” or “output variable.”

Below are a few examples to understand the usage and significance of dependent and independent variables in a wider sense:

• Suppose you want to estimate the cost of living of a person using a regression model. In that case, you need to take independent variables as factors such as salary, age, marital status, etc. The cost of living of a person is highly dependent on these factors. Thus, it is designated as the dependent variable.
• Another scenario is in the case of a student's poor performance in an examination. The independent variable could be factors, for example, poor memory, inattentiveness in class, irregular attendance, etc. Since these factors will affect the student's score, the dependent variable, in this case, is the student's score.
• Suppose you want to measure the effect of different quantities of nutrient intake on the growth of a newborn child. In that case, you need to consider the amount of nutrient intake as the independent variable. In contrast, the dependent variable will be the growth of the child, which can be calculated by factors such as height, weight, etc.

Let us now understand the concept of a regression line.

## What is the difference between Regression and Classification?

Regression and Classification both come under supervised learning methods, which indicate that they use labelled training datasets to train their models and make future predictions. Thus, these two methods are often classified under the same column in machine learning.

However, the key difference between them is the output variable. In regression, the output tends to be numerical or continuous, whereas, in classification, the output is categorical or discrete in nature.

Regression and Classification have certain different ways to evaluate the predictions, which are as follows:

• Regression predictions can be interpreted using root mean squared error, whereas classification predictions cannot.
•  Classification predictions can be evaluated using accuracy, whereas, on the other hand, regression predictions cannot be evaluated using the same.

Conclusively, we can use algorithms like decision trees and neural networks for regression and classification with small alterations. However, some other algorithms are more difficult to implement for both problem types, for example, linear regression for regressive predictive modeling and logistic regression for classification predictive modeling.

## What is a Regression Line?

In the field of statistics, a regression line is a line that best describes the behaviour of a dataset, such that the overall distance from the line to the points (variable values) plotted on a graph is the smallest. In layman's words, it is a line that best fits the trend of a given set of data.

Regression lines are mainly used for forecasting procedures. The significance of the line is that it describes the interrelation of a dependent variable “Y” with one or more independent variables “X”. It is used to minimize the squared deviations of predictions.

If we take two variables, X and Y, there will be two regression lines:

• Regression line of Y on X: This gives the most probable Y values from the given values of X.
• Regression line of X on Y: This gives the most probable values of X from the given values of Y.

The correlation between the variables X and Y depend on the distance between the two regression lines. The degree of correlation is higher if the regression lines are nearer to each other. In contrast, the degree of correlation will be lesser if the regression lines are farther from each other.

If the two regression lines coincide, i.e. only a single line exists, correlation tends to be either perfect positive or perfect negative. However, if the variables are independent, then the correlation is zero, and the lines of regression will be at right angles.

Regression lines are widely used in the financial sector and business procedures. Financial Analysts use linear regression techniques to predict prices of stocks, commodities and perform valuations, whereas businesses employ regressions for forecasting sales, inventories, and many other variables essential for business strategy and planning.

## What is the Regression Equation?

In statistics, the Regression Equation is the algebraic expression of the regression lines. In simple terms, it is used to predict the values of the dependent variables from the given values of independent variables.

Let us consider one regression line, say Y on X and another line, say X on Y, then there will be one regression equation for each regression line:

• ### Regression Equation of Y on X:

This equation depicts the variations in the dependent variable Y from the given changes in the independent variable X. The expression is as follows:

Ye = a + bX

Where,

• Ye is the dependent variable,
• X is the independent variable,
• a and are the two unknown constants that determine the position of the line.

The parameter “a” indicates the distance of a line above or below the origin, i.e. the level of the fitted line, whereas parameter "b" indicates the change in the value of the independent variable Y for one unit of change in the dependent variable X.

The parameters "a" and "b" can be calculated using the least square method. According to this method, the line needs to be drawn to connect all the plotted points. In mathematical terms, the sum of the squares of the vertical deviations of observed Y from the calculated values of Y is the least. In other words, the best-fitted line is obtained when ∑ (Y-Ye)2 is the minimum.

To calculate the values of parameters “a” and “b”, we need to simultaneously solve the following algebraic equations:

Y = Na + b  X

XY = a  X + b  X2

• ### Regression Equation of X on Y:

This equation depicts the variations in the independent variable Y from the given changes in the dependent variable X. The expression is as follows:

Xe = a + bY

Where,

• Xe is the dependent variable,
• Y is the independent variable,
• a and are the two unknown constants that determine the position of the line.

Again, in this equation, the parameter “a” indicates the distance of a line above or below the origin, i.e. the level of the fitted line, whereas parameter "b" indicates the slope, i.e. change in the value of the dependent variable X for a unit of change in the independent variable Y.

To calculate the values of parameters “a” and “b” in this equation, we need to simultaneously solve the following two normal equations:

X = Na + b  Y

XY = a  Y + b  Y2

Please note that the regression lines can be completely determined only if we obtain the constant values “a” and “b”.

## How does Linear Regression work?

Linear Regression is a Machine Learning algorithm that allows an individual to map numeric inputs to numeric outputs, fitting a line into the data points. It is an approach to modeling the relationship between one or more variables. This allows the model to able to predict outputs.

Let us understand the working of a Linear Regression model using an example.

Consider a scenario where a group of tech enthusiasts has created a start-up named Orange Inc. Now, Orange has been booming since 2016. On the other hand, you are a wealthy investor, and you want to know whether you should invest your money in Orange in the next year or not.

Let us assume that you do not want to risk a lot of money, so you buy a few shares. Firstly, you study the stock prices of Orange since 2016, and you see the following figure:

It is indicative that Orange is growing at an amazing rate where their stock price has gone from 100 dollars to 500 dollars in only three years. Since you want your investment to boom along with the company's growth, you want to invest in Orange in the year 2021. You assume that the stock price will fall somewhere around $500 since the trend will likely not go through a sudden change. Based on the information available on the stock prices of the last couple of years, you were able to predict what the stock price is going to be like in 2021. You just inferred your model in your head to predict the value of Y for a value of X that is not even in your knowledge. This mental method you undertook is not accurate anyway because you were not able to specify what exactly will be the stock price in the year 2021. You just have an idea that it will probably be above 500 dollars. This is where Regression plays its role. The task of Regression is to find the line that best fits the data points on the plot so that we can calculate where the stock price is likely to be in the year 2021. Let us examine the Regression line (in red) by understanding its significance. By making some alterations, we obtained that the stock price of Orange is likely to be a little higher than 600 dollars by the year 2021. This example is quite oversimplified, so let us examine the process and how we got the red line on the next plot. ### Training the Regressor The example mentioned above is an example of Univariate Linear Regression since we are trying to understand the change in an independent variable X to one dependent variable, Y. Any regression line on a plot is based on the formula: f(X) = MX + B Where, • is the slope of the line, • B is the y-intercept that allows the vertical movement of the line, • And is the function’s input variable. In the field of Machine Learning, the formula is as follows: h(X) = W0 + W1X Where, • W0 and W1 are the weights, • X is the input variable, • h(X) is the label or the output variable. Regression works by finding the weights W0 and W1 that lead to the best-fitting line for the input variable X. The best-fitted line is obtained in terms of the lowest cost. Now, let us understand what does cost means here. ### The cost function Depending upon the Machine Learning application, the cost could take different forms. However, in a generalized view, cost mainly refers to the loss or error that the regression model yields in its distance from the original training dataset. In a Regression model, the cost function is the Squared Error Cost: J(W0,W1) = (1/2n) Σ { (h(Xi) - Ti)2} for all i =1 until i = n Where, • J(W0, W1) is the total cost of the model with weights W0 and W1, • h(Xi) is the model’s prediction of the independent variable Y at feature X with index i, • Ti is the actual y-value at index i, • and n refers to the total number of data points in the dataset. The cost function is used to obtain the distance between the y-value the model predicted and the actual y-value in the data set. Then, the function squares this distance and divides it by the number of data points, resulting in the average cost. The 2 in the term ‘(1/2n)’ is merely to make the differentiation process in the cost function easier. ### Training the dataset Training a regression model uses a Learning Algorithm to find the weights W0 and W1 that will minimize the cost and plug them into the straight-line function to obtain the best-fitted line. The pseudo-code for the algorithm is as follows: Repeat until convergence { temp0 := W0 - a.((d/dW0) J(W0,W1)) temp1 := W1 - a.((d/dW1) J(W0,W1)) W0 = temp0 W1 = temp1 }  Here, (d/dW0and (d/dW1refer to the partial derivatives of J(W0,, W1concerning W0, and W1 respectively. The gist of the partial differentiation is basically the derivatives: • (d/dW0) J(W0,W1) = W0 + W1.X - T • (d/dW1) j(W0,W1) = (W0 + W1.X - T).X Implementing the Gradient Descent Learning algorithm will result in a model with minimum cost. The weights that led to the minimum cost are dealt with as the final values for the line function h(X) = W0 + W1X. ### Goodness-of-Fit in a Regression Model The Regression Analysis is a part of the linear regression technique. It examines an equation that lessens the distance between the fitted line and all data points. Determining how well the model fits the data is crucial in a linear model. The general idea is that if the deviations between the observed values and the predicted values of the linear model are small and unbiased, the model has well-fit data. In technical terms, “Goodness-of-fit” is a mathematical model describing the differences between the observed and expected values or how well the model fits a set of observations. This measure can be used in statistical hypothesis testing. ## How do businesses use Regression Analysis? Regression Analysis is a statistical technique used to evaluate the relationship between two or more independent variables. Organizations use regression analysis to understand the significance of their data points and use analytical techniques to make better decisions. Business Analysts and Data Professionals use this statistical tool to delete unwanted variables and select the significant ones. There are numerous ways that businesses use regression analysis. Let us discuss some of them below. ### 1. Decision-making Businesses need to make better decisions to run smoothly and efficiently, and it is also necessary to understand the effects of the decision taken. They collect data on various factors such as sales, investments, expenditures, etc. and analyze them for further improvements. Organizations use the Regression Analysis method by making sense of the data and gathering meaningful insights. Business analysts and data professionals use this method to make strategic business decisions. ### 2. Optimization of business The main role of regression analysis is to convert the collected data into actionable insights. The old-school techniques like guesswork and assuming a hypothesis have been eliminated by organizations. They are now focusing on adopting data-driven decision-making techniques, which improves the work performance in an organization. This analysis helps the management sectors in an organization to take practical and smart decisions. The huge volume of data can be interpreted and understood to gain efficient insights. ### 3. Predictive Analysis Businesses make use of regression analysis to find patterns and trends. Business Analysts build predictions about future trends using historical data. Regression methods can also go beyond predicting the impact on immediate revenue. Using this method, you can forecast the number of customers willing to buy a service and use that data to estimate the workforce needed to run that service. Most insurance companies use regression analysis to calculate the credit health of their policyholders and the probable number of claims in a certain period. Predictive Analysis helps businesses to: • Minimize costs • Minimize the number of required tools • Provide fast and efficient results • Detect fraud • Risk Management • Optimize marketing campaigns ### 4. Correcting errors Regression Analysis is not only used for predicting trends, but it is also useful to identify errors in judgements. Let us consider a situation where the executive of an organization wants to increase the working hours of its employees and make them work extra time to increase the profits. In such a case, regression analysis analyses all the variables and it may conclude that an increase in the working hours beyond their existing time of work will also lead to an increase in the operation expense like utilities, accounting expenditures, etc., thus leading to an overall decrease in the profit. Regression Analysis provides quantitative support for better decision-making and helps organizations minimize mistakes. ### 5. New Insights Organizations generate a large amount of cluttered data that can provide valuable insights. However, this vast data is useless without proper analysis. Regression analysis is responsible for finding a relationship between variables by discovering patterns not considered in the model. For example, analyzing data from sales systems and purchase accounts will result in market patterns such as increased demand on certain days of the week or at certain times of the year. You can maintain optimal stock and personnel using the information before a demand spike arises. The guesswork gets eliminated by data-driven decisions. It allows companies to improve their business performance by concentrating on the significant areas with the highest impact on operations and revenue. ## Use cases of Regression Analysis ### Pharmaceutical companies Pharmaceutical organizations use regression analysis to analyze the quantitative stability data for the retest period or estimate shelf life. In this method, we find the nature of the relationship between an attribute and time. We determine whether the data should be transformed for linear regression analysis or non-linear regression analysis using the analyzed data. • ### Finance The simple linear regression technique is also called the Ordinary Least Squares or OLS method. This method provides a general explanation for placing the line of the best fit among the data points. This particular tool is used for forecasting and financial analysis. You can also use it with the Capital Asset Pricing Model (CAPM), which depicts the relationship between the risk of investing and the expected return. • ### Credit Card Credit card companies use regression analysis to analyze various factors such as customer's risk of credit default, prediction of credit balance, expected consumer behaviour, and so on. With the help of the analyzed information, the companies apply specific EMI options and minimize the default among risky customers. ## When Should I Use Regression Analysis? Regression Analysis is mainly used to describe the relationships between a set of independent variables and the dependent variables. It generates a regression equation where the coefficients correspond to the relationship between each independent and dependent variable. ### Analyze a wide variety of relationships You can use the method of regression analysis to perform many things, for example: • To model multiple independent variables. • Include continuous and categorical variables. • Use polynomial terms for curve fitting. • Evaluate interaction terms to examine whether the effect of one independent variable is dependent on the value of another variable. Regression Analysis can untangle very critical problems where the variables are entwined. Consider yourself to be a researcher studying any of the following: • What impact does socio-economic status and race have on educational achievement? • Do education and IQ affect earnings? • Impact of exercise habits and diet affect weight. • Do drinking coffee and smoking cigarettes reduce the mortality rate? • Does a particular exercise have an impact on bone density? These research questions create a huge amount of data that entwines numerous independent and dependent variables and question their influence on each other. It is an important task to untangle this web of related variables and find out which variables are statistically essential and the role of each of these variables. To answer all these questions and rescue us in this game of variables, we need to take the help of regression analysis for all the scenarios. ### Control the independent variables Regression analysis describes how the changes in each independent variable are related to the changes in the dependent variable and how it is responsible for controlling every variable in a regression model. In the process of regression analysis, it is crucial to isolate the role of each variable. Consider a scenario where you participated in an exercise intervention study. You aimed to determine whether the intervention was responsible for increasing the subject's bone mineral density. To achieve an outcome, you need to isolate the role of exercise intervention from other factors that can impact the bone density, which can be the diet you take or any other physical activity. To perform this task, you need to reduce the effect of the unsupportive variables. Regression analysis estimates the effect the change in one dependent variable has on the dependent variables while all other independent variables are constant. This particular process allows you to understand each independent variable's role without considering the other variables in the regression model. Now, let us understand how regression can help control the other variables in the process. According to a recent study on the effect of coffee consumption on mortality, the initial results depicted that the higher the intake of coffee, the higher is the risk of death. However, researchers did not include the fact that most coffee drinkers smoke in their first model. After smoking was included in the model, the regression results were quite different from the initial results. It depicted that coffee intake lowers the risk of mortality while smoking increases it. This model isolates the role of each variable while holding the other variables constant. You can examine the effect of coffee intake while controlling the smoking factor. On the other hand, you can also look at smoking while controlling for coffee intake. This particular example shows how omitting a significant variable can produce misleading results and causes it to be uncontrolled. This warning is mainly applicable for observational studies where the effects of omitted significant variables can be unbalanced. This omitted variable bias can be minimized in a randomization process where true experiments tend to shell out the effects of these variables in an equal manner. ### What are Residuals in Regression Analysis? Residuals identify the deviation of observed values from the expected values. They are also referred to as error or noise terms. It gives an insight into how good our model is against the actual value, but there are no real-life representations of residual values. Calculating the real values of intercept, slope, and residual terms can be a complicated task. However, the Ordinary Least Square (OLS) regression technique can help us speculate on an efficient model. The technique minimizes the sum of the squared residuals. With the help of the residual plots, you can check whether the observed error is consistent with stochastic error (differences between the expected and observed values must be random and unpredictable). ## What are the Linear model assumptions in Regression Analysis? Regression Analysis is the first step in the process of predictive modeling. It is quite easy to implement, and its syntax and parameters do not create any kind of confusion. However, the purpose of regression analysis is not just solved by running a single line of code. It is much more than that. The function plot(model_name) returns four plots in the R programming language. Each of these plots provides essential information about the dataset. Most beginners in the field are unable to trace the information. But once you understand these plots, you can bring important improvements to your regression model. For significant improvements in your regression model, it is also crucial to understand the assumptions you need to take in your model and how you can fix them if any assumption gets violated. The four assumptions that should be met before conducting linear regression are as follows: 1. Linear Relationship: A linear relationship exists between the independent variable, x, and the dependent variable, y. 2. Independence: The residuals in linear regression are independent. In other words, there is no correlation between consecutive residuals in time series data. 3. Homoscedasticity: Residuals have constant variance at every level of X. 4. Normality: The residuals of the model are normally distributed. ### Assumption 1: Linear Relationships #### Explanation The first assumption in Linear regression is that there is a linear relationship between the independent variable X and the dependent variable Y. #### How to determine if this assumption is met The quickest and easiest way to detect this assumption is by creating a scatter plot of X vs Y. By looking at the scatter plot, you can have a visual representation of the linear relationship between the two variables. If the points in the plot could fall along a straight line, then there exists some type of linear relationship between the variables, and this assumption is met. For example, consider this first plot below. The points in the plot look like they fall roughly on a straight line, which indicates that there exists a linear relationship between X and Y: However, there doesn’t appear to be a linear relationship between X and Y in this second plot below: And in this third plot, there appears to be a clear relationship between X and Y, but a linear relationship between: #### What to do if this assumption is violated If you create a scatter plot between X and Y and do not find any linear relationship between the two variables, then you can do two things: • You can apply a non-linear transformation to the dependent or independent variables. Common examples might include taking the log, the square root, or the reciprocal of the independent and dependent variable. • You can add another independent variable to the regression model. If the plot of X vs Y has a parabolic shape, then adding Xas an additional independent variable in the linear regression model might make sense. ### Assumption 2: Independence #### Explanation The second assumption of linear regression is that the residuals should be independent. Its relevance can be seen while working with time-series data. In an ideal manner, a pattern among consecutive residuals is not what we want. For example, in a time series model, the residuals should not grow steadily along with time. How to determine if this assumption is met To determine if this assumption is met, we need to have a scatter plot of residuals vs time and look at the residual time series plot. In an ideal plot, the residual autocorrelations should fall within the 95% confidence bands around zero, located at about +/- 2-over the square root on n, where n denotes the sample size. You can also perform the Durbin-Watson test to formally examine if this assumption is met. What to do if this assumption is violated If this assumption is violated, you can do three things which are as follows: • If there is a positive serial correlation, you can add lags of the independent variable or dependent variable to the regression model. • If there is a negative serial correlation, check that none of the variables has differences. • If there is a seasonal correlation, consider adding a seasonal dummy variable into your regression model. ### Assumption 3: Homoscedasticity #### Explanation The third assumption of linear regression is that the residuals should have constant variance at every level of X. This property is called homoscedasticity. When homoscedasticity is not present, the residuals suffer from heteroscedasticity. The outcome of the regression analysis becomes hard to trust when heteroscedasticity is present in the model. It increases the variance of the regression coefficient estimates, but the model does not recognize this fact. This makes the model declare that a term in the model is significantly crucial, but it is not. #### How to determine if this assumption is met To determine if this assumption is met, we need to have a scatter plot of fitted values vs residual plots. To achieve this, you need to fit a regression line into a data set. Below is a scatterplot showing a typical fitted value vs residual plot in which heteroscedasticity is present: You can observe how the residuals become much more spread out as the fitted values get larger. The “cone” shape is a classic sign of heteroscedasticity: #### What to do if this assumption is violated If this assumption is violated, you can do three things which are as follows: • Transform the dependent variable: The most common transformation is simply taking the dependent variable's log. Consider if you are using population size as an independent variable to predict the number of flower shops in a city as the dependent variable. You need to use population size to predict the number of flower shops in a city. It causes heteroscedasticity to go away. • Redefine the dependent variable: One common way is to use a rate rather than the raw value. Consider the previous example. In that case, use population size to predict the number of flower shops per capita instead. This reduces the variability that naturally occurs among larger populations. • Use weighted regression: The third way to fix heteroscedasticity is to use weighted regression. In this regression method, we assign a weight to each data point depending on the variance of its fitted value, giving small weights to data points having higher variances, which shrinks their squared residuals. When the proper weights are used, the problem of heteroscedasticity gets eradicated. ### Assumption 4: Normality #### Explanation We need to take the last assumption that the residuals should be normally distributed. How to determine if this assumption is met To determine if this assumption is met, there are two common ways to achieve that: 1. Use Q-Q plots to examine the assumption visually. Also known as the quantile-quantile plot, it is used to determine whether or not the residuals of the regression model follow a normal distribution. The normality assumption is achieved if the points on the plot roughly form a straight diagonal line as follows: However, this Q-Q plot below shows when the residuals clearly deviate from a straight diagonal line, they do not follow a normal distribution: 2. Some other formal statistical tests to check the normality assumption are Shapiro-Wilk, Kolmogorov-Smirnov, Jarque-Barre, and D'Agostino-Pearson. These tests however have a limitation as they are used only when there are large sample sizes and it often results that the residuals are not normal. Therefore, graphical techniques like Q-Q plots are easier to check the normality assumption and are also more preferable. #### What to do if this assumption is violated If this assumption is violated, you can do two things which are as follows: • Firstly, examine if outliers are present and exist, make sure they are real values and aren’t data errors. Also, verify that any outliers aren’t having a large impact on the distribution. • Secondly, you can apply a non-linear transformation to the independent and/or dependent variables. Common examples include taking the log, the square root, or the reciprocal of the independent and/or dependent variable. ## How to perform a simple linear regression? The formula for a simple linear regression is: Y = B0 + B1X + e Where, • Y refers to the predicted value of the dependent variable Y for any given value of the independent variable X. • B0 denotes the intercept, i.e. the predicted value of y when the x is 0. • B1 denotes the regression coefficient, i.e. how much we expect the value of y to change as the value of x increases. • X refers to the independent variable, or the variable we expect is influencing y). • e denotes the error estimate, i.e. how much variation exists in our regression coefficient estimate. The Linear regression model's task is to find the best-fitted line through the data by looking out for the regression coefficient B1 that minimizes the total error estimate e of the model. ### Simple linear regression in R R is a free statistical programming language that most data professionals use very powerful and widely. Let us consider a dataset of income and happiness that we will use to perform regression analysis. The first task is to load the income.data dataset into the R environment, and then generate a linear model describing the relationship between income and happiness by the command as follows: income.happiness.lm <- lm(happiness ~ income, data = income.data) The code above mentioned takes the data that has been collected using data = income.data. Then, it estimates the impact of the independent variable income on the dependent variable happiness using the linear model equation: lm() ### Interpreting the results To obtain and visualize the results of the simple linear regression model, you can use the summary() function in R by executing the following code: summary(income.happiness.lm)  What this function does is it takes the essential factors from the linear model and puts them into a tabular form, which looks like this: According to the output table, the first thing it does is repeat the formula used to generate the results (‘Call’). The next thing it does is summarize the model residuals (‘Residuals’), which explains how well the model fits the real data. Next, you can see the Coefficients table. The first row of this table provides the estimates of the y-intercept, and the second row provides the regression coefficient of the model. The first row of the Coefficients’ table is labelled (Intercept), the Y-intercept of the regression equation, with a value of 0.20. Now, if you want to predict the happiness values across the range of observed values of income, you need to insert this into your regression equation : happiness = 0.20 + 0.71*income ± 0.018 The next row in the ‘Coefficients’ table is income that describes the estimated effect of income on reported happiness. The Estimate column is the estimated effect or the regression coefficient (R2) value. The table (0.713) indicates that for every unit increase in income, there is a corresponding 0.71-unit increase in reported happiness. The column of Std. Error displays the standard error of the estimate, which shows how much variation there is in the estimate of the relationship between income and happiness. The t value column displays the test statistic. The test statistic used in a linear regression model is the t-value from a two-sided t-test unless specified otherwise. The results depend on the test statistic. The larger the test statistic, the less probable that our results occurred by chance. The Pr(>| t |) column displays the p-value, which tells us how probable we are to see the estimated effect of income on happiness considering the null hypothesis of no effect were true. We can reject the null hypothesis since the p-value is very low (p < 0.001), and finally, we can conclude that income has a statistically crucial effect on happiness. The most important thing here in the linear regression model is the p-value. In this example, it is quite significant (p < 0.001), which shows that this model is a good fit for the observed data. ### Presenting the results While presenting your results, you should include the regression coefficient, standard error of the estimate, and the p-value. You should also interpret your numbers so that readers can have a clear understanding of the regression coefficient: A significant relationship (p < 0.001) has been found between income and happiness (R2 = 0.71 ± 0.018), with a 0.71-unit increase in reported happiness for every$10,000 increase in income.

For a simple linear regression, you can simply plot the observations on the x and y-axis of a scatter plot and then include the regression line and regression function.

## What is multiple regression analysis?

Multiple Regression is an extension of simple linear regression and is used to estimate the relationship between two or more independent variables and one dependent variable.

You can perform multiple regression analysis to know:

• The strength of the relationship between one or more independent variables and one dependent variable. For example, you can use it to understand whether the exam performance can be predicted based on revision time, test anxiety, lecture attendance, and gender.
• The overall fit, i.e. variance of the model and the relative impact of each of the predictors to the total variance explained. For example, you might want to know how much of the variation in the student’s exam performance can be understood by revision time, test anxiety, lecture attendance, gender, and the relative impact of each independent variable in explaining the variance.

## How to perform multiple linear regression?

The formula for multiple linear regression is:

Y = B0 + B1X1 + … + BnXn + e

Where,

• Y refers to the predicted value of the dependent variable Y for any given value of the independent variable X.
• B0 denotes the intercept, i.e. the predicted value of y when the x is 0.
• B1X denotes the regression coefficient (B1), i.e. how much we expect the value of Y to change as the value of X increases.
• ... does the same for all the independent variables we want to test.
• BnXn refers to the regression coefficient of the last independent variable
• e denotes the error estimate of the model, i.e. how much variation exists in our estimate of the regression coefficient.

It is the task of the Multiple Linear regression model to find the best-fitted line through the data by calculating the following three things:

• The regression coefficients will lead to the least error in the overall multiple regression model.
• The t-statistic of the overall regression model.
• The associated p-value

The multiple regression model also calculates the t-statistic and p-value for each regression coefficient.

### Multiple linear regression in R

Let us consider a dataset of the heart and other factors that affect the functioning of our heart to perform multiple regression analyses.

The first task is to load the heart.data dataset into the R environment, and then generate a linear model describing the relationship between heart disease and biking to work by the command as follows:

heart.disease.lm<-lm(heart.disease ~ biking + smoking, data = heart.data)

The code above mentioned takes the data that has been collected using data = heart.data. Then, it estimates the impact of the independent variable biking and smoking on the dependent variable heart disease using the linear model equation:

lm()

### Interpreting the results

To obtain and visualize the results of the simple linear regression model, you can use the summary() function in R by executing the following code:

summary(heart.disease.lm)

What this function does is it takes the essential factors from the linear model and puts them into a tabular form, which looks like this:

According to the output table, the first thing it does is repeat the formula used to generate the results (‘Call’). The next thing it does is summarize the model residuals (‘Residuals’), which explains how well the model fits the real data.

If the residuals are roughly centred around zero and with a similar spread on either side, then the model probably fits the assumption of heteroscedasticity.

Next, you can see the ‘Coefficients’ table. The first row of this table provides the estimates of the y-intercept, and the second row provides the regression coefficient of the model.

The first row of the ‘Coefficients’ table is labelled (Intercept), the Y-intercept of the regression equation. Now, if you want to predict the biking and smoking values across the range of observed values of heart, you need to insert this into your regression equation :

heart disease = 15 + (-0.2*biking) + (0.178*smoking) ± e

The Estimate column is the estimated effect or the regression coefficient  (R2) value. The estimates in the table tell us that for every 1% increase in biking to work, there is an associated 0.2 % decrease in heart disease. For every 1% increase in smoking, there is an associated 0.17 % increase in heart disease.

The column of Std. Error displays the standard error of the estimate, which shows how much variation there is in the estimate of the relationship between income and happiness.

The t value column displays the test statistic. The test statistic used in a  linear regression model is the t-value from a two-sided t-test unless specified otherwise. The results depend on the test statistic. The larger the test statistic, the less probable that our results occurred by chance.

The Pr(>| t |) column displays the p-value, which tells us how probable we are to see the estimated effect of income on happiness considering the null hypothesis of no effect were true.

We can reject the null hypothesis since the p-value is very low (p < 0.001), and finally, we can conclude that both - biking to work and smoking - have influenced rates of heart disease.

The most important thing here in the linear regression model is the p-value. In this example, it is quite significant (p < 0.001), which shows that this model is a good fit for the observed data.

### Presenting the results

While presenting your results, you should include the regression coefficient, standard error of the estimate, and the p-value. You should also interpret your numbers in the proper context so that readers can have a clear understanding of the regression coefficient:

In our survey of 500 towns, we found significant relationships between the frequency of biking to work and the frequency of heart disease and the frequency of smoking and heart disease (p < 0.001 for each). Specifically, we found a 0.2% decrease (± 0.0014) in the frequency of heart disease for every 1% increase in biking and a 0.178% increase (± 0.0035) in the frequency of heart disease for every 1% increase in smoking.

For multiple linear regression, you can simply plot the observations on the X and Y-axis of a scatter plot and then include the regression line and regression function:

In this example, we have calculated the predicted values of the dependent variable heart disease across the observed values for the percentage of people biking to work.

However, to include the effect of smoking on the independent variable heart disease, we had to calculate the predicted values by holding the variable smoking as constant at the minimum, mean, and maximum observed smoking rates.

## What is R-squared in Regression Analysis?

In data science, R-squared (R2) is the coefficient of determination or the coefficient of multiple determination in case of multiple regression.

In the linear regression model, R-squared acts as an evaluation metric to evaluate the scatter of the data points around the fitted regression line. It recognizes the percentage of variation of the dependent variable.

### R-squared and the Goodness-of-fit

R-squared is the proportion of variance in the dependent variable that the independent variable can explain.

The value of R-squared stays between 0 and 100%:

• 0% corresponds to a model that does not explain the variability of the response data around its mean. The mean of the dependent variable helps predict the dependent variable and the regression model.
• On the other hand, 100% corresponds to a model that explains all the variability of the response variable around its mean.

If your value of R is large, you have a better chance of your regression model fitting the observations.

Although you get essential insights about the regression model in this statistical measure, you should not depend on it for the complete assessment of the model. It lacks information about the relationship between the dependent and the independent variables.

It also does not inform about the quality of the regression model. Hence, as a user, you should always analyze Rand other variables and then derive conclusions about the regression model.

### Visual Representation of R-squared

You can visually demonstrate the plots of fitted values by observed values in a graphical manner. It illustrates how R-squared values represent the scatter around the regression line.

As observed in the pictures above, the value of R-squared for the regression model on the left side is 17%, and for the model on the right is 83%. When the variance accounts to be high in a regression model, the data points tend to fall closer to the fitted regression line.

However, a regression model with an R2 of 100% is an ideal scenario that is impossible. In such a case, the predicted values equal the observed values, leading all the data points to fall exactly on the regression line.

### Interpretation of R-squared

The simplest interpretation of R-squared is how good the regression model fits the observed data values. Let us loot at an example to understand this.

Consider a model where the  R2  value is 70%. This would mean that the model explains 70% of the fitted data in the regression model. Usually, when the R value is high, it suggests a better fit for the model.

The correctness of the statistical measure does not only depends on R2. Still, it can depend on other several factors like the nature of the variables, the units on which the variables are measured, etc. So, a high R-squared value is not always likely for the regression model and can indicate problems too.

A low R-squared value is a negative indicator for a model in general. However, if we consider the other factors, a low Rvalue can also result in a good predictive model.

### Calculation of R-squared

R- squared can be evaluated using the following formula:

Where:

• SSregression – Explained sum of squares due to the regression model.
• SStotal  The total sum of squares.

The sum of squares due to regression assesses how well the model represents the fitted data. The total sum of squares measures the variability in the data used in the regression model.

Now let us come back to the earlier situation where we have two factors: the number of hours of study per day and the score in a particular exam to understand the calculation of R-squared more effectively. Here, the target variable is represented by score and the independent variable by the number of study hours per day.

In this case, we will need a simple linear regression model and the equation of the model will be as follows:

ŷ = w1x1 + b

The parameters wand can be calculated by reducing the squared error over all the data points. The following equation is called the least square function:

minimize ∑(yi –  w1x1i – b)

Now, R-squared calculates the amount of variance of the target variable explained by the model, i.e. function of the independent variable.

However, to achieve that, we need to calculate two things:

• Variance of the target variable:

var(avg) = ∑(yi – Ӯ)2

• The variance of the target variable around the best-fit line:

var(model) = ∑(yi – ŷ)2

Finally, we can calculate the equation of R-squared as follows:

R2 = 1 – [var(model)/var(avg)] = 1 -[∑(yi – ŷ)2/∑(yi – Ӯ)2]

## What are the different types of regression analysis?

Other than simple linear regression and multiple linear regression, there are mainly 5 types of regression techniques. Let us discuss them one by one.

### Polynomial Regression

In a polynomial regression technique, the power of the independent variable has to more than 1. The expression below shows a polynomial equation:

y = a + bx2

In this regression technique, the best-fitted line is a curve line instead of a straight line that fits into the data points.

An important point to keep in mind while performing polynomial regression is, if you try to fit a polynomial of a higher degree to get a lower error, it might result in overfitting.  You should always plot the relationships to see the fit and always make sure that the curve fits the nature of the problem. An example to illustrate how plotting can help:

### Logistic Regression

The logistic regression technique is used when the dependent variable is discrete in nature. For example, 0 or 1, true or false, etc. The target variable in this regression can have only two values and the relation between the target variable and the independent variable is denoted by a sigmoid curve.

To measure the relationship between the target variable and independent variables,

Logit function is used. The expression below shows a logistic equation:

logit(p) = ln(p/(1-p)) = b+ b1X+ b2X+ b3X…. + bkXk

Where,

p denotes the probability of occurrence of the feature.

### Ridge Regression

The Ridge Regression technique is usually used when there is a high correlation between the independent variables. This is because the least square estimates result in unbiased values when there are multi collinear data.

However, if the collinearity is very high, there exists some bias value. Therefore, it is crucial to introduce a bias matrix in the equation of Ridge Regression. This regression method is quite powerful where the model is less susceptible to overfitting.

The expression below shows a ridge regression equation:

β = (X^{T}X + λ*I)^{-1}X^{T}y

The lambda (λ) in the equation solves the issue of multicollinearity.

### Lasso Regression

Lasso Regression is one of the types of regression in machine learning that is responsible for performing regularization and feature selection. It restricts the absolute size of the regression coefficient, due to which the coefficient value gets nearer to zero.

The feature selection method in Lasso Regression allows the selection of a set of features from the dataset to build the model. Only the required features are used in this regression, while others are made zero. This helps in avoiding overfitting in the model.

If the independent variables are highly collinear, then this regression technique takes only one variable and makes other variables shrink to zero.

The expression below shows a lasso regression equation:

N^{-1}Σ^{N}_{i=1}f(x_{i}, y_{I}, α, β)

### Bayesian Regression

In the Bayesian Regression method, the Bayes theorem is used to determine the value of regression coefficients. In this linear regression technique, the posterior distribution of the features is evaluated other than finding the least-squares.

Bayesian Linear Regression collaborates with Linear Regression and Ridge Regression but is more stable than simple Linear Regression.

## What are the terminologies used in Regression Analysis?

When trying to understand the outcome of regression analysis, it is important to understand the key terminologies used to acknowledge the information.

A comprehensive list of regression analysis terms used are described below:

• ### Estimator:

An estimator is an algorithm for generating estimates of parameters when the relevant dataset is present.

• ### Bias:

An estimate is said to be unbiased when its expectation is the same as the value of the parameter that is being estimated. On the other hand, if the expectation is the same as the value of the estimated parameter, it is said to be biased.

• ### Consistency:

An estimator is consistent if the estimates it produces converge on the value of the true parameter considering the sample size increases without limit. For example, an estimator that produces estimates θ^ for some value of parameter θ, where is a small number. If the estimator is consistent, we can make the probability as close to 1.0 or as small as we like by drawing a sufficiently large sample.

• ### Efficiency:

An estimator “A” is said to be more efficient than an estimator “B” when “A” has a smaller sampling variance, i.e. if the specific values of “A” are more tightly clustered around their expectation.

• ### Standard error of the Regression (SER):

It is defined as estimating the standard deviation of the error term in a regression model.

• ### Standard error of regression coefficient:

It is defined as estimating the standard deviation of the sampling distribution for a particular coefficient term.

• ### P-value:

P-value is the probability when the null hypothesis is considered true, of drawing sample data that are as adverse to the null as the data drawn, or more so. When the p-value is small, there are two possibilities for that – firstly, a low-probability unrepresentative sample is drawn, or secondly, the null hypothesis is false.

• ### Significance level:

For a hypothesis test, the significance test is the smallest p-value for which the null hypothesis is not rejected. If the significance level is 1%, the null is rejected if and only if the p-value for the test is less than 0.01. The significance level can also be defined as the probability of making a type 1 error, i.e. rejecting a true null hypothesis.

• ### Multicollinearity:

It is a situation where there is a high degree of correlation among the independent variables in a regression mod. In other words, a situation where some of the X values are close to being linear combinations of other X values. Multicollinearity occurs due to large standard errors and when the regression model cannot produce precise parameter estimates. This problem mainly occurs while estimating causal influences.

• ### T-test:

The t-test is a common test for the null hypothesis that Bi's particular regression parameter has some specific value.

• ### F-test:

F-test is a method for jointly testing a set of linear restrictions on a regression model.

• ### Omitted variable bias:

Omitted variable bias is a bias in estimating regression parameters. It generally occurs when a relevant independent variable is omitted from a model, and the omitted variable is correlated with one or more of the included variables.

• ### Log variables:

It is a transformation method that allows the estimation of a non-linear model using the OLS method to exchange the natural log of a variable for the level of that variable. It is performed for the dependent variable and/or one or more independent variables.

This is another common transformation method where both xand x2i are included as regressors. The estimated effect of xi on is calculated by finding the derivative of the regression equation concerning xi

• ### Interaction terms:

These are the pairwise products of the "original" independent variables. The interaction terms allow for the possibility that the degree to which xi affects depends on the value of some other variable Xj. For example, the effect of experience on wages xi might depend on the gender xj of the worker.

## What are the tips to avoid common problems working with regression analysis?

Regression is a very powerful statistical analysis that offers high flexibility but presents a variety of potential pitfalls. Let us see some tips to overcome the most common problems whilst working with regression analysis.

• ### Tip 1:  Research Before Starting

Before you start working with regression analysis, review the literature to understand the relevant variables, the relationships they have, and the expected coefficient signs and effect magnitudes. It will help you collect the correct data and allow you to implement the best regression equation.

• ### Tip 2: Always prefer Simple Models

Start with a simple model and then make it more complicated only when needed. When you have several models with different predictive abilities, always prefer the simplest model because it will be more likely to be the best model. Another significant benefit of simpler models is that they are easier to understand and explain to others.

• ### Tip 3: Correlation Does Not Imply Causation

Always remember correlation doesn't imply causation. Causation is a completely different thing as compared to causation. In general, to establish causation, you need to perform a designed experiment with randomization. However, If you’re using regression analysis to analyze the uncollected data in an experiment, causation is uncertain.

• ### Tip 4: Include Graphs, Confidence, and Prediction Intervals in the Results

The presentation of your results can influence the way people interpret them. For instance, confidence intervals and statistical significance provide consistent information.  According to a study, statistical reports that refer only to statistical significance only bring about correct interpretations 40% of the time. On the other hand, when the results also include confidence intervals, the percentage rises to 95%.

• ### Tip 5: Check the Residual Plots

Residual plots are the quickest and easiest method to examine the problems in a regression model and allow you to make adjustments. For instance, residual plots help display patterns when you cannot model curvature present in your data.

## Regression Analysis and The Real World

Let us summarize what we have covered in this article so far:

• Regression Analysis and its importance.
• Difference between regression and classification.
• Regression Line and Regression Equation.
• How companies use regression analysis
• When to use regression analysis.
• Assumptions in Regression Analysis.
• Simple and Multiple linear regression.
• R-squared: Representation, Interpretation, Calculation.
• Types of Regression.
• Terminologies used in Regression.
• How to avoid problems in regression.

Regression Analysis is an interesting machine learning technique utilized extensively by enterprises to transform data into useful information. It continues to be a significant asset to many leading sectors starting from finance, education, banking, retail, medicine, media, etc.

### Priyankur Sarkar

Data Science Enthusiast

Priyankur Sarkar loves to play with data and get insightful results out of it, then turn those data insights and results in business growth. He is an electronics engineer with a versatile experience as an individual contributor and leading teams, and has actively worked towards building Machine Learning capabilities for organizations.

## How to Become a Data Scientist

According to a recent Harvard Business Review article, being a Data Scientist is the coolest job of the 21st century. Fom startups to Fortune 500 companies, everyone is looking out for the best and brightest of individuals to fill up the role of a Data Scientist.  There are several questions that arise for anyone wanting to become a Data Scientist. What is Data Science? What are the roles and responsibilities of a Data Scientist? How does one become a Data Scientist and what are the skills required for it? And many more. In this article, we will answer all the questions about a career in Data Science and take you a step forward towards becoming a successful Data Scientist.Let us first get an understanding of why Data Science is important. What is the need for Data Science? Traditionally, the data that was generated was small in size and structured in its outlook. Simple Business Intelligence could be used to analyze such datasets. With time, data has become significantly unstructured or semi-structured. This is because the data generated in recent times is vast and collected from multiple sources like text files, financial documents, multimedia data, sensors, etc. BI tools are not able to process this huge and varied amount of data. In order to gather insights from these data, we need advanced analytical tools and algorithms. This is one of the major reasons for the growth in popularity of Data Science.  Data Science allows an individual to make better decisions by performing predictive analysis and finding significant patterns. Some of the key things you can do with the help of data science are: Asking the right questions and finding the cause of a problem Performing an exploratory study on the data Data modeling with the help of multiple algorithms Data visualization using graphs, charts, dashboards, etc. What is Data Science? Data Science is a practice that helps you to generate insights from structured, semi-structured, and unstructured datasets with the help of various scientific techniques and algorithms which in turn allows you to make predictions and plan out data-driven solutions. In coordination with different statistical tools, it works on a huge amount of data to provide such meaningful insights for better decision making.  Let us understand Data Science better with an example. Consider your sleep quality, for instance.  The kind of sleep you had last night tends to be 1 data point for every day. On day 1, you had an excellent sleep of 8 hours. You did not move much, nor did you awaken much. That’s a data point. However, on day 2, you slept lightly for just 7 hours. That is another data point.By collecting and analyzing such data points for a whole month, you can gather insights about your sleeping pattern. Maybe, around the weekdays, you have 6 - 7 hours of sleep and on the weekends, you have 8 hours of sleep. Also, you can gather other insights, say, around  2 a.m. every night, you have most of the short awakenings in a week. If you work on the data of your sleep quality for a year, you can gather more complex analyses. You can learn what would be the best time for you to go to sleep and wake up or you could identify the worst sleeping time of the year and correlate it to work pressure. Further, you can even predict such stressful parts of the year and allow yourself to be prepared beforehand.  The data we use in Data Science projects is usually gathered from numerous sources ranging from surveys, social media platforms, e-commerce websites, browsing searches, etc. We are able to access all these data because of the latest and advanced technologies used in recent times for data collection. Small and big businesses both benefit from this data because they allow the organizations to make predictions about the products and make informed decisions which in turn gives huge profit returns to the business giants.What is the role of a Data Scientist? The role of a data scientist is becoming more significant since most businesses are dependent on data science to drive their decision-making and most of the IT strategies lean on machine learning and automation.  Data Scientists are considered to be big data wranglers. They gather and analyze large chunks of structured and unstructured data. Their role involves the collaboration of computer science, statistics, and mathematics. They perform analysis, processing, and modeling of the data and finally interpret the results in order to create actionable plans for business organizations.  In basic terms, a Data Scientist organizes and analyzes large amounts of data with specific software designed for a specific task. They discover insights from data to meet specific business needs and targets. They are mostly analytical experts who utilize their industry knowledge, contextual understanding, and skills in technology and social science to find trends and uncover solutions to business problems. The data on which a typical Data Scientist works is usually unstructured and messy, collected from multiple sources like social media platforms, smart devices and emails and their task is to make sense out of that data. However, technical skills are not the only thing that is required in a Data Scientist. A Data Scientist is also expected to be an effective communicator, leader, team member, and work as a high-level analytical thinker. This is because they usually belong in business settings and are given the duty to communicate complex ideas and make business decisions depending upon data trends.  Experienced data scientists are often tasked to work with other teams in their organization, such as marketing, operations, or customer success. They perform tasks starting from cleaning up data, to processing it, and finally storing the data.  A Data Scientist is one of the most highly sought after job roles at present, in a tech-dependent economy; and their salaries and the growth of job is clearly a reflection of that.  Let us look at the basic responsibilities of a Data Scientist. What are the responsibilities of a Data Scientist? An important step towards becoming a Data Scientist is to understand the numerous responsibilities they need to undertake in their journey. Some of the most common responsibilities are as follows: Management – A Data Scientist plays a managerial role by supporting the construction of the pillars of the technical abilities within the Data and Analytics field which allows them to provide assistance to many planned and active data projects. Analytics – A Data Scientist plans, implements, and assesses statistical models and strategies which are applicable in the most complex issues of a business. They develop models for numerous problems such as projections, classification, clustering, pattern analysis, etc. Strategy or Design – In order to understand the trends of consumers, a Data Scientist plays a significant aspect in the progress of innovative strategies. It also helps data scientists to provide solutions to difficult business challenges, for example, how to optimize the process of product fulfillment and the entire profit generation. Collaboration – The key role of a Data Scientist is to enhance an organization’s performance scale and help in better decision making. To achieve these, a data scientist needs to collaborate with other experienced data scientists and discuss various obstructions and findings with the relevant stakeholders. Knowledge – A Data Scientist takes initiative to look into numerous other tools and technologies so that they can create innovative meaningful insights for the business organization. They also assess and make use of new and enhanced data science methods to pace up the business tactics.  Let us now take a look at the most popular industries that hire Data Scientists. What are the top industries hiring Data Scientists? Since the evolution of Data Science, it has been helpful in tackling many real-world challenges and is in great demand across a wide range of industries which allows business giants to become more intelligent and make better-informed decisions. This is the reason why Data Science and big data analytics are at the cutting edge of every industry. The top industries that hire data scientists are as follows: Retail – Big Data and Analytics provide meaningful insights to the retail industry which is a major reason behind their customer’s happiness and it allows them to retain their customers. According to a study by IBM, around 62% of retail respondents claim that information provided by Data Scientists allowed them to have advantages over other business giants.  Banking and Finance – In the recent era, bankers have started to use technologies to drive their decision-making process. The Bank of America has created a virtual assistant named Erica using natural language processing and predictive analytics, which helps customers to access information about their forthcoming bills and also view previous transactions. They also believe that it will gradually be able to suggest financial schemes to customers at appropriate times by studying the habits of a customers’ banking. Medicine –  This industry is making use of data and analytics to improve healthcare in a lot of ways. One example of such is the use of wearable trackers. It provides meaningful information to physicians who in turn can provide better care for their patients. It also provides data about whether the patient is taking the medication or not and also whether the patient is following the proper treatment plan or not.   Communication, Media, and Entertainment – Data Science is being used in this field to gather data from social media platforms and mobile content and understand real-time media usage patterns. One such example is Spotify, which is an on-demand music streaming service application. It collects and analyzes data from its users to render them with their specific taste of music. Education –  Data Science in this sector can be used for a number of tasks. A data science model can measure a teachers’ effectiveness by measuring against many factors like each individual subject, the number of students, aspirations of students, student demographics, and other related variables. The University of Tasmania developed a learning and management system model with the help of 26,000 students. This particular system can track the time of a student login, students’ overall progress, and time spent on other different pages. Transportation – Data Science is used by transportation providers to help people reach their destinations on time. They enhance the chances of successful trips by gathering data such as traffic time, rush hours, etc. The Transport department of London has devised a statistical model which gives them information about customer journeys and how they can manage unpredicted situations and provide people with individual transport details.  Outsourcing – The Outsourcing industries make use of Data Science to automatize the back-office processing, controls price-checking, and also helps to reduce the turnaround time. Flatworld Solutions is a business company who have incorporated Data Science in their systems to automate processes like classification and indexing of documents, naming and processing of PDF files, discovering related documents, and also for inventory management. Let us now take a look at the most popular industries that hire Data Scientists. What are the key skills to master to become a Data Scientist?Data Science has taken over the corporate world and every tech enthusiast is eager to learn the top skills to become a Data Scientist. It is one of the fastest-growing career fields with a job growth of around 650% since the year 2012 and a median salary of around $125,000. Data Science helps you to extract the knowledge from data to answer your question. In layman’s terms, it is a powerful tool that businesses and stakeholders use to make better choices and to solve real-world problems. So, as we learn new technologies and more difficult challenges come our way, it becomes significant for us to build a strong base. Let us learn in detail about the key skills you need to have to become a Data Scientist in the 21st century. 1. Education According to a study, Data Scientists are usually highly educated with around 88% of them having a Master’s degree and around 50% of them PhDs. Though there are a number of exceptions, in order to develop the deep knowledge necessary for a Data Scientist, you need to have a very strong educational background. You can have a lot of options in choosing your field. You can earn a Bachelor’s degree in Computer Science, or Statistics, or you can even opt for Social Sciences and Physical Sciences. The most popular fields of study that will provide you the skills to become a Data Scientist are Mathematics and Statistics (32%), Computer Science (19%), and Engineering (16%). However, earning a bachelor’s degree is not enough. Most Data Scientists working in the field enroll themselves into a number of other training programs to learn an outside skill, for example, Hadoop or Big Data querying, alongside their Master’s degree and PhDs. So you can do your Master’s program in any field like Mathematics, Data Science, or Statistics and allow yourself to engage in learning some extra skills which in turn will help you to easily shift your career to being a Data Scientist. Apart from your academic degree and extra skills, you can also learn to channel your skills in a practical way by taking on small projects such as creating an app, writing blogs, or even exploring data analysis to gather more information. 2. FundamentalsAs a beginner in the field of Data Science, you would be suggested by many to learn machine learning techniques like Regression, Clustering, or SVM without having any basic understanding of the terminologies. This would be a very bad way to start your journey in the field of Data Science since promises of “Build your ML model in just 5 lines of code” are far-fetched from reality. The first and the most essential skill you need to develop at the beginning of your journey is to know about the fundamentals of Data Science, Artificial Intelligence, and Machine Learning. To understand the basics, you should focus on topics that answer the following questions: What is the difference between Machine Learning and Deep Learning? What is the difference between Data Science, Data Analysis, and Data Engineering? What are fundamental tools and terminologies relevant to Data Science? What is the difference between Supervised and Unsupervised Learning? What are Classification and Regression problems? 3. MathematicsData Science is all about using algorithms to extract insights from data and make data-driven informed decisions. This is because making inferences, estimating, or predicting is a significant part of Data Science. Data Scientists need to have a very strong foundation of the following mathematical concepts: Probability – In order to work as a Data Scientist, you need to learn about concepts such as Bayes’ Theorem, Distribution functions, Central Limit Theorem, expected values, standard errors, random variables, and independence. These concepts of probability will help you to perform statistical tests on data and uncover insights from it. Statistics – Data Scientists should be well aware of the key concepts in Statistics which include mean, median, mode, maximum likelihood indicators, standard deviation, distributions, and sampling techniques. You should also learn about Descriptive statistics and Inferential statistics which will help to get a brief idea of the data through charts and graphs and also you can make predictions using that data respectively. Multivariable Calculus – As you aspire to be a Data Scientist, you need to brush up your concepts on mean value theorems, gradient, derivatives, limits, Taylor series, and finally beta and gamma functions. These concepts will help you to understand logistic regression algorithms and also help in solving different calculus challenges in interviews. Linear Algebra – It is considered to be the backbone of the essential machine learning algorithms and concepts like matrices and vectors will help you in the long run. Other than the above concepts, some of the complimentary topics you can learn are step function, sigmoid function, logit function, Rectified Linear Unit function, cost function, and tensor functions. Plotting of functions is also an important skill to learn alongside all these You can refer to the following links to learn about the Mathematics for Data Science: Coursera’s Mathematics for Data Science MIT course on Linear Algebra Harvard’s Data Science: Probability 4. Python & R programming According to a survey by O’Reilly, 40% of respondents claim that they use Python as their major programming language. It is considered to be the most commonly used and most efficient coding language for a Data Scientist along with Java, Perl, or C/C++. Python is a versatile programming language and can be used for performing all the tasks of a Data Scientist. You can collect a lot of data formats using Python and can easily import SQL tables into your code. Data Scientists can also create datasets using Python. According to another study, 43% of Data Scientists solve various statistical problems with the help of the R programming language. R is the most preferred programming tool to gather a deep knowledge of any analytical tools and you can use it to solve any problem while working with Data Science. However, in comparison to Python, R has a very steep learning curve. You can refer to the following links to learn about Python and R: Google’s Python Class Udemy’s Introduction to Data Science using Python Coursera’s R programming 6. Hadoop Platform Hadoop is an open-source software library created by the Apache Software Foundation. According to a survey performed by CrowdFlower on around 3490 LinkedIn data science jobs, Hadoop was claimed to be the second most important skill for a Data Scientist with a rating of 49 percent. It is basically used to distribute big data processing across a range of computing devices. The Hadoop platform has its own Hadoop Distributed File System (HDFS) to store large data and is also used to stream the data to user applications like MapReduce. Though it does not come under a requirement, having some user experience with software like Hive, Pig, or Hoop is a strong point in your resume. You should make yourself familiar with cloud tools like Amazon S3. The role of Hadoop comes when you are faced with a circumstance where the memory of your system is being exceeded by the large volume of data or in other situations such as when you need to send data to a number of different servers. It can also be used for data exploration, data sampling, data filtration, and summarization. You can refer to the following links to learn about Hadoop: Big Data and Analytics by IBM Udacity’s Introduction to Hadoop and MapReduce 7. SQL Database SQL or Structured Query Language is a programming language that allows a user to store, query, and manipulate data in relational database management systems. You can perform operations like addition, deletion, and extraction of data from a database and also carry out analytical functions and modification of database structures. Though NoSQL and Hadoop have resulted to become essential components of data science, a candidate aspiring to be a Data Scientist should learn to write and execute complex SQL queries. SQL software is particularly designed to help individuals access, communicate, and work on data easily. It provides insights and consists of comprehensive commands that help to reduce work time and also decrease the amount of programming needed for difficult search queries. As a Data Scientist, you need to be quite proficient in the use of SQL, and learning it will develop a better understanding of relational database systems and also boost your profile as a Data Scientist. You can refer to the following links to learn about SQL: Coursera’s SQL for Data Science Oracle SQL 8. Apache Spark Apache Spark is a processing engine and is becoming one of the most renowned big data technologies in the global market. It can easily integrate with Hadoop and can work with large and unstructured datasets. However, the only difference between them is that Spark is much faster than Hadoop. The reason behind this is that Spark stores its computations in its memory while Hadoop reads and writes to disk, making it slower. Data Scientists work with Spark due to its specific design and it helps to run complex algorithms much faster than other tools. They use it to handle large chunks of complex unstructured datasets and disseminate the data processing. Spark can be used on a single machine or a cluster of machines. Performing data analytics and distributing computing is a simple task in Spark. The X factor of this software lies in its speed and platform which allows Data Scientists to prevent any loss of data and also carrying out Data Science projects becomes easier. You can refer to the following links to learn about SQL: Spark Starter Kit Hadoop Platform and Application Framework 8. Machine Learning and Artificial Intelligence Although all data science roles are not required to have knowledge of deep learning, data engineering skills, or Natural language Processing, if you want to stand out in a crowd of data Scientists, you need to be acquainted with the techniques of Machine Learning like Supervised Machine learning, decision trees, logistic regression, k-nearest neighbors, random forests, ensemble learning, etc. According to a survey by Kaggle, a small percentage of Data professionals are competent in advanced machine learning skills which include Supervised and Unsupervised machine learning, Time series, Natural language processing, Outlier detection, Computer vision, Recommendation engines, Survival analysis, Reinforcement learning, and Adversarial learning. If you are interested in working with big data and want to solve different data science problems, you should make yourself familiar with Machine Learning techniques. You can refer to the following links to learn about Machine Learning: Elements of AI Machine Learning course from Stanford HarwardX’s Data Science 9. Data VisualizationA popular idiom says “A picture is worth a thousand words”. Data Visualization is a graphical representation of data and an essential skill to learn for a Data Scientist. People understand visuals in the form of charts and graphs much better in comparison to raw data. So the huge amount of data being produced by businesses needs to be transformed into a form that is easily understood by people. You need to learn different Data Visualization tools such as ggplot, Power BI, Matplotlib, and Tableau. As a Data Scientist, these tools will allow you to convert your raw form of data into a certain format for people to understand more easily. Most people do not understand datasets of serial correlation or p values, so it becomes essential to translate these data which is visually more representable so that you can make comparisons and predictions out of it. Almost all business organizations make use of data visualization tools to grasp meaningful information which in turn helps them to work on new business innovations. You can refer to the following link to learn about Data Visualization tools: Coursera’s course on Data Visualization 10. Intellectual Curiosity Curiosity is the desire of an individual to acquire more knowledge, not just about a particular subject but about a wide range of topics and ideas. An intellectually curious person is someone who has a love for learning. As a Data Scientist, you are expected to ask a lot of questions regarding data since the main job of a Data Scientist is to spend most of the time discovering and preparing the data. Curiosity is one such skill that you need to develop from the beginning to succeed as a Data Scientist. To achieve that, you need to update yourself with all the relevant books, articles, and blogs that are published on the internet about the trends in data science. It is quite essential for you to make sense out of the vast amount of knowledge hovering around the internet. In early stages, you might not be able to extract many insights from your collected data. However, with a curious approach, you will eventually sift through the data to find more answers.11. Business Acumen As a Data Scientist, you need to have a clear understanding of how businesses operate so as to make sure your efforts are channeled in the right direction. Having a precise perspective of the industry you are working in is essential so that you can solve the business problems of your company. It is important as a Data Scientist to be able to recognize which problems to solve for your organization and identify new techniques as to how your problem-solving can be beneficial for the business. 12. Communication Skills and Teamwork Good communication skills can help you to easily and clearly translate technical insights for non-technical people like a member from the Marketing or Sales department. It is essential for a data scientist to understand the needs of their non-technical fellow workers. They perform this task by wrangling the data in a suitable manner and generate critical insights enabling the businesses to take informed solutions. Storytelling around the data is another skill you need to learn as a Data Scientist to make it easy for others to understand. It is important as it allows you to properly convey your findings to other team members. For example, sharing information from your data in a storytelling method is much more effective to understand and gather in comparison to a simple table of data. As a Data Scientist, you have to work with literally everyone, from company executives to develop strategies, designers to create better products, marketers for better product campaigns, and clients and developers to create data pipelines and improve the flow of work. Last but not the least, as a Data Scientist, you need to develop use cases with your fellow members so as to gather information about the business goals and data to solve the real-world challenges. You have to keep in mind the right approach to address the use cases and how you can convey your result in a way that can be easily understood by everyone involved in the process. What are the Data Scientists’ salaries around the world? According to a report by Glassdoor, Data Scientist has been named the number one job in the US for four years in a row. Furthermore, the U.S. Bureau of Labor Statistics stated that the data science skills will boost a 27.9 percent rise in employment by the year 2026. Although the demand for Data Scientists is high, there is a shortage of qualified data scientists globally. In recent times, every business organization extracts information from sales or marketing campaigns and uses this data to gather insights. These insights allow the business to answer questions like what worked well, what did not, and what to do differently in the future. Thus, businesses can make more informed decisions with the right and organized data. The salaries of Data Scientists depend on several factors like which industry they are working in, how many years of experience they have, what is the size of the organization, and so on. However, one big advantage of being a Data Scientist is they are always in demand globally and if you get bored of working in a particular city or a particular country, you always have the option of moving somewhere else because of the freedom and flexibility that this role offers. Let us now look at the highest paying countries and the average annual salary of a Data Scientist: India – The average annual Data Scientist salary in India is over ₹698,412. The USA – The average annual Data Scientist salary in the USA is around USD 120,122. Germany – The average annual Data Scientist salary in Germany is around €55,440. United Kingdom – The average annual Data Scientist salary in the UK is around £40423. Canada – The average annual Data Scientist salary in Canada is around CAD 79123. Australia – The average annual Data Scientist salary in Australia is over AUD 115,000. Denmark – The average annual Data Scientist salary in Denmark is around DKK 44,344. Singapore – The average annual Data Scientist salary in Singapore is around SGD 70,975. What factors affect the salary of a Data Scientist in India?According to Glassdoor, Data Scientists in India have a base pay ranging between 3 – 10 Lakhs. A Data Scientist in India with experience between 1 – 4 years has a net earning of around ₹6,10,811 per annum. On the other hand, an individual with experience of 5 – 9 years makes up to 10,04,082 per annum and someone with more experience than that can earn up to 17,00,700 per annum in India. However, there are several factors that are also associated while deciding the salary of a Data Scientist. Every company, big or small, around the world now considers data science as an important sector and looks upon its potential to be able to change the market trends. The decision-making authorities of the companies are focusing more on technology and consumers. Now, let us understand what are the significant factors that affect the salary of a Data Scientist in India.1. Based on Experience According to a survey by Linkedin, an entry-level Data Scientist having a Master’s degree and experience of 1 – 5 years can get an annual salary of around 9 lakhs and can earn up to 11 lakhs for another couple of years of experience. A senior Scientist gets an annual salary of around 20 lakhs or more with experience of 6 – 14 years. However, someone with a specialization in the field can get a salary of around 23 lakhs or more. Let’s see how experience affects the salary of a Data Scientist in India: The average annual salary of an Entry-Level Data Scientist in India is ₹5,11,648. The average annual salary of a mid-Level Data Scientist in India is ₹13,67,306. The average annual salary of an experienced Data Scientist in India is ₹24,44,000 2. Based on IndustryEvery industry around the world recruits Data Scientists, due to which, there has been a significant increase of individuals choosing this career path which in turn adds a lot of value and enhances the progress of different industries. In an organization, the Data Scientists are directly responsible for most of the decision-making process and they achieve this with the help of meaningful information using statistical tools like Power BI, Tableau, and SQL. The progress impacts the salaries of these Data Scientists which range between$80,000 to $107,000 at their entry level. Financial companies hire Data Scientists to predict the company’s performance by gathering knowledge about the macroeconomic and microeconomic trends. The Scientists in this industry are responsible for creating economic data models and forecasts. Data Scientists working in this sector have an average annual salary ranging between$60,500 to $72,000. Marketing research Scientists use sales data, customer surveys, and competitor research to optimize the targeting and positioning efforts of their products. This industry has a pay scale ranging from$61,490 to $75,000 at the entry-level.Similarly, the Data Scientists working in the healthcare industry, whose job is to maintain the daily administrative advancements and operations gets an average annual salary of$60,000 to $85,000.3. Based on LocationThe highest number of Data Scientists and the average annual data salary in India is the highest in the Silicon Valley of India, a.k.a Bangalore. Bangalore, Pune, and Gurgaon offer 22.2%, 10.5%, and 10.5% more than the average annual salary in India respectively. On the other hand, Data Scientists working in Mumbai get a salary ranging between 3.5 lakh to 20 lakh per annum which is less than the national average. Hyderabad and New Delhi receive 7.65 and 4.7% less than the national average respectively. 4. Based on CompanyThe top recruiters of Data Scientists in India are tech giants like Tata Consultancy Services, Fractal Analytics, Accenture, and Cognizant whereas according to reports, salaries offered are highest at Microsoft which is around 7 Lakhs – 28 Lakhs per annum. Source link: Payscale.com 5. Based on Skills Skill is an important factor while deciding the salary of a Data Scientist in India. You need to go beyond the qualifications of a Master’s degree and Ph.D. and gather more knowledge of the respective languages and software.Source link: Payscale.com Some useful insights are as follows: The most important skill is to have a clear understanding of Python. A python programmer in India alone earns around 10.5 Lakhs per annum. There is an increase of around 25 percent in the salary of a Data Scientist in India when you get familiar with Big Data and Data Science. Experts in Statistical Package for Social Sciences or SPSS get an average salary of 7.3 Lakhs whereas experts in Statistical Analysis Software or SAS have an earning of around 9 Lakhs to 10.8 Lakhs. A Machine Learning expert in India alone can earn around 17 Lakhs per year. Being a Data Scientist, if you learn ML and Python alongside, you can reach the highest pay in this field. Which are the top countries where Data Scientists are in demand? According to a global study by Capgemini, almost half of the global organizations have agreed that the gap between the skilled and the not-so-skilled is not only huge but is widening with the years. With the increase in the application of Machine Learning and Artificial Intelligence, there is a spike in demand for skilled IT professionals across the globe. As the demand for data science has emerged, there has been a shortage of skills in this sector making this a huge concern for the tech giants. As the demand and the supply gap has widened, there has been a plethora of opportunities for data scientists all over the world. Let us see some of the top geographies where Data Scientists are in high demand. 1. Europe Almost every major tech hub in Europe, from Berlin, Amsterdam, London, Paris, to Stockholm, has a great demand for data science professionals. The most rigorous technical jobs in Europe include Artificial Intelligence, Machine Learning, Deep Learning, Cloud Security to Robotics, and Blockchain technologies. Among the leading digitally-driven countries in Europe, Sweden has the highest demand for Data Science professionals. The demand for IT skills and the shortage of data science professionals has compelled European countries to fill the vacancies from outside the European nations. According to a German study, by the year 2020, they will face a shortage of 3 million skilled workers, with an appreciable number of them being IT professionals.2. United Kingdom The United Kingdom has a vast demand for Machine Learning skilled professionals, which has nearly tripled in the last five years reaching around 231%. According to a survey, recruitment specialists in the United Kingdom claim that the demand for Artificial Intelligence skills is growing much faster than in countries like the US, Australia, and Canada. In 2018, the number of AI vacancies in the United Kingdom was 1300 out of every million. This was double the vacancies produced in Canada and almost 20% more than in the US. Different regions saw different growth rates, for example, in Wales, it rose to 79% and to 269% in the North West regions in the UK. 3. India India is considered to be the testing ground of most of the applications of Data Science starting from security to healthcare to media. The IT industry of India is expected to have a requirement of around 50% of professionals with data skills. The ratio of skilled individuals to the jobs available in the Deep Learning field is around 0.53 and for machine learning, the figure stands at 0.63. This shows the demand for professionals with skills in Artificial Intelligence, Machine Learning, and user interface. The regions in India where data professionals are highest in demand are Mumbai, Pune, Delhi, Bangalore, Chennai, and Hyderabad and the hiring industries include IT, healthcare, e-commerce, retail, etc. 4. ChinaChina is one of the top countries that have a high demand for professionals in the Artificial Intelligence field. They are active participants in this sector and investing heavily in innovations such as facial-recognition eyewear for police officers which will help them to locate wanted criminals. Although the demand for AI professionals is high in China, they face an acute shortage due to which the job market is unable to fill up vacant job positions. Data Science professionals who have at least 5 years of experience in the field are a rare sight, so companies in China are continuously looking for skilled individuals all over the world and are readily active to give much higher average salaries than most countries.5. Canada Canada aspires to reach the top position in the development of Artificial Intelligence in the global market. They have started investing heavily to create a framework on ethics, policy, and the legal inference of AI. The topmost demanding data science jobs in Canada are Machine Learning Engineer, Full Stack Developer, and DevOps Engineer. Professionals with experience of around 1 – 5 years can earn a salary of$70,000 to $90,000 per annum. Furthermore, an individual with more than 5 years of experience can earn up to$130,000 or more. What are the different career pathways starting from Data Scientist? Learning data science skills is a way to overturn your journey in this field. But landing your dream job can take some time, even if you have mastered your skills in Python, R, SQL, and other technical tools. You need to invest time, effort, and build requisite knowledge to find a job that’s right for you.  The first step in the process is to identify the different types of jobs that you should be looking for.  Let us talk about some of the in-demand roles in the data science world which you can undertake starting from a Data Scientist. Machine Learning Engineer Average Salary The average salary of a Machine Learning Engineer in the US is $144,800. What is a machine learning engineer? All machine learning engineers are needed to have at least some of the data science skills and a good advanced understanding of machine learning techniques. At some companies, this title means an individual who is a data scientist having some specialization in machine learning whereas, at some other companies, it might mean a software engineer performing data analysis and turning it into some deployable software. There is always an overlap between a machine learning engineer and a data scientist. Quantitative Analyst Average Salary The average salary of a Quantitative Analyst in the US is$127,400. What is a Quantitative Analyst?  Quantitative Analysts are also referred to as “quants”. Their main job is to make predictions related to finance and risk using advanced statistical tools. A strong foundation of statistics is essential in this field and most of the data science skills are vastly beneficial for a Quantitative Analyst. Knowledge of Machine learning models and how they can be used to figure out financial challenges are increasingly common these days.  Business Intelligence Analyst  Average Salary The average salary of a Business Intelligence Analyst in the US is $95,800.Who is a Business Intelligence Analyst? A business intelligence analyst is essentially a data analyst whose job is to analyze data to gather meaningful market and business trends. This particular position is required to have knowledge on how to use software-based data analysis tools, for example, Power BI and Tableau. Most of the data science skills are also significant for a business intelligence analyst along with solid foundational skills in Python and R programming. Data Warehouse Architect Average Salary The average salary of a Data Warehouse Architect in the US is$134,373. Who is a Data Warehouse Architect?  A data warehouse architect is essentially in charge of a company’s data storage systems. Although it is a sub-category within Data Engineering, SQL and database management skills are quite crucial for this position. You will not be hired as a data warehouse architect solely on the basis of your data science skills. If you want to work as a data warehouse architect in the data engineering sector, you need to have a command over different technical skills.  Statistician Average Salary The average salary of a Statistician in the US is $99,300. Who is a Statistician? ‘Statistician’ is the name of the job title that data scientists were called before the term ‘data science’ even existed. The necessary skill required for all statisticians is a strong foundation of probability and statistics, although it might vary from one job to another. Knowledge of any statistical-based programming language like R will also be beneficial for this job role. Although they are expected to have an understanding of the mathematical techniques of different machine learning models, they are not required to build and train machine learning models. Systems Analyst Average Salary The average salary of a Systems Analyst in the US is$79,470. Who is a Systems Analyst?  The main task of a Systems Analyst is to discover organizational challenges and then plan and examine the changes or the new systems that are important for problem-solving. For this job role, you need to be familiar with programming skills, data science skills, and few statistical skills. All these skills combined will help you identify the issues in your company's technical system and allow you to make decisions about what to implement and what not to.Operational Analyst Average Salary The average salary of an Operation Analyst in the US is $67,250.Who is an Operational Analyst? The main task of an Operational Analyst is to examine and organize the internal processes of a business organization. All operational analysts are not required to make use of data science skills, but in most cases, their major focus is on cleaning, analyzing, and visualizing the data. It allows them to determine which of the company systems are working efficiently and which of the parts require improvements. How to transition into Data Science from other career domains? With a steady rise in demand and popularity, a lot of young professionals want to pursue a career in data science. It helps that the field offers perks and a plethora of job openings all over the world. Organizations are trying to stay ahead of their competitors by investing heavily towards acquiring data science talent. That said, the transition into Data Science has its own set of challenges. Let us look at how individuals working in other career domains like IT, Sales, Finance, HR, or Healthcare can transition into the world of Data Science. 1. From Software Engineer to a Data Scientist If you really enjoy working as a software engineer, you should consider the most common role of a Data Engineer or a Machine Learning Engineer. However, if you are keen on working as a Data Scientist, you need to acquire these skills: Probability and Statistics – Learn the fundamental concepts of probability and statistics.SQL – As a software engineer, you have already learned database management. You now need to learn about concepts like window functions, CTEs, triggers, and style guides of SQL, etc. Data Modeling –You need to study some good data models and also learn how and when to use them. You can take the help of e-documentations and tutorials available on the internet. Make sure to have an understanding of the domain you are working in, such as healthcare, logistics, manufacturing, etc.Data Visualization – You should learn how to visualize your data with the help of graphs, charts, time series, or other visualization tools. Reporting – After you have gathered insights, learn how to compile and organize them into a report, for example, a document or a dashboard. Communication – It is one of the most important skills you need to develop in the process. Your fellow workers should understand your analysis in a very easy and efficient manner. 2. From Finance to a Data Scientist If you’re from a finance background, you are very close to your dream of becoming a data scientist. It is a field of numbers and easily blends with the data science space. However, if you are willing to work as a Data Scientist in finance, you need to acquire these skills: First of all, you need to acquire a degree in mathematics, statistics, computer science, physics, or engineering. You should be able to program in a number of programming languages like C or C++, Python, R, and Java. You have to learn database skills like SQL in any of the database management systems like MySQL, Oracle, or SQL Server. Finally, you need to learn to handle time-series data from any financial data channels like Bloomberg, Reuters, etc. Other than these skills, you need to work on your mathematical skills both verbally and visually and how to solve commercial challenges using them. Also, have a strong foundation of concepts like optimization, statistical inference, multivariate analysis, and so on. 3. From UX Designer/Researcher to a Data Scientist UX researchers have already been using low hang data science tools like Google Analytics, Excel, JSON, user testing data, etc. These tools and techniques are significant in doing UX designs and finding insights into the data. However, if you're willing to dig deep into data science tools and languages, you need to learn advanced Excel functions, Tableau, learn to code in JavaScript, and also learn to work with data libraries such as d3.js and R programming. 4. From Application Development to a Data Scientist The role of an application developer is to develop a webpage that is understandable by the stakeholders. On the other hand, a Data Scientist's job is to give an output in numbers and present these numbers to the customers with a visual aid. However, to transition from an application developer to a data scientist, the best way is to start learning the fundamentals of Data Science, Machine Learning, Statistics, and Database Management and work your way up in the field. 5. From Marketing and Sales to a Data Scientist Amongst all other career domains mentioned earlier, a Marketing and Sales professional is widely different. However, a Marketing and Sales team is mostly dependent on data and gets the opportunity to work closely with data analysts. So, a transition from this field into data science can be a natural changeover. Apart from all these factors, you need to keep in mind some of the realities about an analytics job when switching to a role in Data Science: A Data Science job is starkly different from sales and marketing roles You have to acquire skills in mathematics, statistics, programming, etc. You need to have better decision-making skills requiring a business-focused attitude. You need to learn organizational thinking. You need to be a keen and fast learner and be able to work with terminologies like regression, decision trees, graphs, and charts most of the time. 6. From no technical background to a Data Scientist This is one of the most common and popular question asked everywhere - Can I become a Data scientist without a technical or an engineering background? The simple and short answer is Yes! According to experts in the field, you actually do not require any background as such to become a Data Scientist. The only thing you require is a keen interest in the subject and asking yourself the question of whether you want to work with data and make an effect in your organization’s decision-making process. However, as a beginner in the field, without any prior experience, you can follow this learning process: First of all, learn programming be it Python or R, and try to become proficient in that language. Secondly, gather knowledge on the following subjects - Probability, Statistics, Linear Algebra, Machine Learning Algorithms, and Methods. Finally, after having learned all these, start working on independent projects and focus more on the basic objectives of these projects. What are the top reasons for you to become a Data Scientist?Data science is a multidisciplinary study of data where mathematics, statistics, and computer science collaborate in a single place. It had emerged as the most sought-after job in the 21st century mainly because of lucrative pay and a multitude of job positions. Let us take a look at the key advantages of data science: 1. Highly-in-demand field Data Science is a highly employable and appealing field according to the latest industry trends and claims to create approximately 11.5 million jobs by the year 2026. 2. Highly paid and diverse roles According to Glassdoor, a Data Scientist can earn up to$116,000 on an average per annum. As Data Analytics takes the middle stage in the decision-making process, the demand for data scientists is booming at a high pace and different kinds of job positions are coming up day by day. There is an abundance of data science roles all over the globe. 3. Evolving workplace environments With advanced machine learning algorithms and robotic science, more and more manual and day-to-day tasks are getting automated. Technologies have allowed training models to perform iterative chores and the critical thinking and problem-solving roles are taken up by humans. 4. Improving product standards With the help of machine learning, e-commerce sites are now able to customize their products and enhance consumer experiences. Companies like Amazon and Flipkart use recommendation systems to refer products and give personalized suggestions to users. 5. Invigorating businessData scientists extract useful information from large chunks of data and provide crucial insights to their senior staff members so that they can take better decisions for the organization. Some of the industries benefiting from this are healthcare, finance, management, banking, and e-commerce. 6. Helping the world Predictive analytics and machine learning algorithms have allowed Data Scientists to develop systems which can detect early tumors, anomalies of organs, etc. It is also helping farmers from all over the world by adopting new scientific methods to deal with agricultural pests and insects. How KnowledgeHut can you shape a career in Data Science? KnowledgeHut has various courses by which you can enhance your knowledge on the field of Data Science and which will help you grab a role of Data Scientist in any of the popular industry. Here are some of the Data Science tutorials offered by KnowledgeHut along with their key learning points and ratings:Data Science with Python Certification  42 hrs of live instructor-led training by certified Python experts Visualize data using advanced libraries like Pandas, Matplotlib, Scikit Rating – 4.5 Python for Data Science 24 hours of Instructor-led Training with Hands-on Exercises Analyze and Visualize Data with Python libraries Rating – 4.5 Machine Learning with Python  50 hrs instructor led training along with 45 hrs Python hands on 80 hrs of Python assignments with code review by professionals Rating – 4.5 Introduction to Data Science certification  Your launchpad to a data science career Get mentored by data science experts Rating – 4.5 Data Science Career Track Bootcamp  140 hours of live and interactive sessions by industry experts Immersive Learning with guided Hands-on Exercises (Cloud Labs) Rating – 4.0 Data Science with R Data manipulation, data visualization and more 40 hours of live and interactive instructor-led training Rating – 4.5 Machine Learning with R Certification  Create real world, intelligent R applications 50 hrs. of hands on training from machine learning experts Rating – 4.5 Deep Learning Certification  Become Deep Learning expert by working on real-life case studies 40 hours of Instructor-led Training with Hands-on Python Rating – 4.5
5364
How to Become a Data Scientist