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What is Linear Regression in Machine Learning

Machine Learning, being a subset of Artificial Intelligence (AI), has been playing a dominant role in our daily lives. Data science engineers and developers working in various domains are widely using machine learning algorithms to make their tasks simpler and life easier. For example, certain machine learning algorithms enable Google Maps to find the fastest route to our destinations, allow Tesla to make driverless cars, help Amazon to generate almost 35% of their annual income, AccuWeather to get the weather forecast of 3.5 million locations weeks in advance, Facebook to automatically detect faces and suggest tags and so on.In statistics and machine learning, linear regression is one of the most popular and well understood algorithms. Most data science enthusiasts and machine learning  fanatics begin their journey with linear regression algorithms. In this article, we will look into how linear regression algorithm works and how it can be efficiently used in your machine learning projects to build better models.Linear Regression is one of the machine learning algorithms where the result is predicted by the use of known parameters which are correlated with the output. It is used to predict values within a continuous range rather than trying to classify them into categories. The known parameters are used to make a continuous and constant slope which is used to predict the unknown or the result.What is a Regression Problem?Majority of the machine learning algorithms fall under the supervised learning category. It is the process where an algorithm is used to predict a result based on the previously entered values and the results generated from them. Suppose we have an input variable ‘x’ and an output variable ‘y’ where y is a function of x (y=f{x}). Supervised learning reads the value of entered variable ‘x’ and the resulting variable ‘y’ so that it can use those results to later predict a highly accurate output data of ‘y’ from the entered value of ‘x’. A regression problem is when the resulting variable contains a real or a continuous value. It tries to draw the line of best fit from the data gathered from a number of points.For example, which of these is a regression problem?How much gas will I spend if I drive for 100 miles?What is the nationality of a person?What is the age of a person?Which is the closest planet to the Sun?Predicting the amount of gas to be spent and the age of a person are regression problems. Predicting nationality is categorical and the closest planet to the Sun is discrete.What is Linear Regression?Let’s say we have a dataset which contains information about the relationship between ‘number of hours studied’ and ‘marks obtained’. A number of students have been observed and their hours of study along with their grades are recorded. This will be our training data. Our goal is to design a model that can predict the marks if number of hours studied is provided. Using the training data, a regression line is obtained which will give minimum error. This linear equation is then used to apply for a new data. That is, if we give the number of hours studied by a student as an input, our model should be able to predict their mark with minimum error.Hypothesis of Linear RegressionThe linear regression model can be represented by the following equation:where,Y is the predicted valueθ₀ is the bias term.θ₁,…,θn are the model parametersx₁, x₂,…,xn are the feature values.The above hypothesis can also be represented byWhere, θ is the model’s parameter vector including the bias term θ₀; x is the feature vector with x₀ =1Y (pred) = b0 + b1*xThe values b0 and b1 must be chosen so that the error is minimum. If sum of squared error is taken as a metric to evaluate the model, then the goal is to obtain a line that best reduces the error.If we don’t square the error, then the positive and negative points will cancel each other out.For a model with one predictor,Exploring ‘b1’If b1 > 0, then x (predictor) and y(target) have a positive relationship. That is an increase in x will increase y.If b1 < 0, then x (predictor) and y(target) have a negative relationship. That is an increase in x will decrease y.Exploring ‘b0’If the model does not include x=0, then the prediction will become meaningless with only b0. For example, we have a dataset that relates height(x) and weight(y). Taking x=0 (that is height as 0), will make the equation have only b0 value which is completely meaningless as in real-time height and weight can never be zero. This resulted due to considering the model values beyond its scope.If the model includes value 0, then ‘b0’ will be the average of all predicted values when x=0. But, setting zero for all the predictor variables is often impossible.The value of b0 guarantees that the residual will have mean zero. If there is no ‘b0’ term, then the regression will be forced to pass over the origin. Both the regression coefficient and prediction will be biased.How does Linear Regression work?Let’s look at a scenario where linear regression might be useful: losing weight. Let us consider that there’s a connection between how many calories you take in and how much you weigh; regression analysis can help you understand that connection. Regression analysis will provide you with a relation which can be visualized into a graph in order to make predictions about your data. For example, if you’ve been putting on weight over the last few years, it can predict how much you’ll weigh in the next ten years if you continue to consume the same amount of calories and burn them at the same rate.The goal of regression analysis is to create a trend line based on the data you have gathered. This then allows you to determine whether other factors apart from the amount of calories consumed affect your weight, such as the number of hours you sleep, work pressure, level of stress, type of exercises you do etc. Before taking into account, we need to look at these factors and attributes and determine whether there is a correlation between them. Linear Regression can then be used to draw a trend line which can then be used to confirm or deny the relationship between attributes. If the test is done over a long time duration, extensive data can be collected and the result can be evaluated more accurately. By the end of this article we will build a model which looks like the below picture i.e, determine a line which best fits the data.How do we determine the best fit line?The best fit line is considered to be the line for which the error between the predicted values and the observed values is minimum. It is also called the regression line and the errors are also known as residuals. The figure shown below shows the residuals. It can be visualized by the vertical lines from the observed data value to the regression line.When to use Linear Regression?Linear Regression’s power lies in its simplicity, which means that it can be used to solve problems across various fields. At first, the data collected from the observations need to be collected and plotted along a line. If the difference between the predicted value and the result is almost the same, we can use linear regression for the problem.Assumptions in linear regressionIf you are planning to use linear regression for your problem then there are some assumptions you need to consider:The relation between the dependent and independent variables should be almost linear.The data is homoscedastic, meaning the variance between the results should not be too much.The results obtained from an observation should not be influenced by the results obtained from the previous observation.The residuals should be normally distributed. This assumption means that the probability density function of the residual values is normally distributed at each independent value.You can determine whether your data meets these conditions by plotting it and then doing a bit of digging into its structure.Few properties of Regression LineHere are a few features a regression line has:Regression passes through the mean of independent variable (x) as well as mean of the dependent variable (y).Regression line minimizes the sum of “Square of Residuals”. That’s why the method of Linear Regression is known as “Ordinary Least Square (OLS)”. We will discuss more in detail about Ordinary Least Square later on.B1 explains the change in Y with a change in x  by one unit. In other words, if we increase the value of ‘x’ it will result in a change in value of Y.Finding a Linear Regression lineLet’s say we want to predict ‘y’ from ‘x’ given in the following table and assume they are correlated as “y=B0+B1∗x”xyPredicted 'y'12Β0+B1∗121Β0+B1∗233Β0+B1∗346Β0+B1∗459Β0+B1∗5611Β0+B1∗6713Β0+B1∗7815Β0+B1∗8917Β0+B1∗91020Β0+B1∗10where,Std. Dev. of x3.02765Std. Dev. of y6.617317Mean of x5.5Mean of y9.7Correlation between x & y0.989938If the Residual Sum of Square (RSS) is differentiated with respect to B0 & B1 and the results equated to zero, we get the following equation:B1 = Correlation * (Std. Dev. of y/ Std. Dev. of x)B0 = Mean(Y) – B1 * Mean(X)Putting values from table 1 into the above equations,B1 = 2.64B0 = -2.2Hence, the least regression equation will become –Y = -2.2 + 2.64*xxY - ActualY - Predicted120.44213.08335.72468.36591161113.6471316.2881518.9291721.56102024.2As there are only 10 data points, the results are not too accurate but if we see the correlation between the predicted and actual line, it has turned out to be very high; both the lines are moving almost together and here is the graph for visualizing our predicted values:Model PerformanceAfter the model is built, if we see that the difference in the values of the predicted and actual data is not much, it is considered to be a good model and can be used to make future predictions. The amount that we consider “not much” entirely depends on the task you want to perform and to what percentage the variation in data can be handled. Here are a few metric tools we can use to calculate error in the model-R – Square (R2)Total Sum of Squares (TSS): total sum of squares (TSS) is a quantity that appears as part of a standard way of presenting results of such an analysis. Sum of squares is a measure of how a data set varies around a central number (like the mean). The Total Sum of Squares tells how much variation there is in the dependent variable.TSS = Σ (Y – Mean[Y])2Residual Sum of Squares (RSS): The residual sum of squares tells you how much of the dependent variable’s variation your model did not explain. It is the sum of the squared differences between the actual Y and the predicted Y.RSS = Σ (Y – f[Y])2(TSS – RSS) measures the amount of variability in the response that is explained by performing the regression.Properties of R2R2 always ranges between 0 to 1.R2 of 0 means that there is no correlation between the dependent and the independent variable.R2 of 1 means the dependent variable can be predicted from the independent variable without any error. An R2 between 0 and 1 indicates the extent to which the dependent variable is predictable. An R2 of 0.20 means that there is 20% of the variance in Y is predictable from X; an R2 of 0.40 means that 40% is predictable; and so on.Root Mean Square Error (RMSE)Root Mean Square Error (RMSE) is the standard deviation of the residuals (prediction errors). The formula for calculating RMSE is:Where N : Total number of observationsWhen standardized observations are used as RMSE inputs, there is a direct relationship with the correlation coefficient. For example, if the correlation coefficient is 1, the RMSE will be 0, because all of the points lie on the regression line (and therefore there are no errors).Mean Absolute Percentage Error (MAPE)There are certain limitations to the use of RMSE, so analysts prefer MAPE over RMSE which gives error in terms of percentages so that different models can be considered for the task and see how they perform. Formula for calculating MAPE can be written as:Where N : Total number of observationsFeature SelectionFeature selection is the automatic selection of attributes for your data that are most relevant to the predictive model you are working on. It seeks to reduce the number of attributes in the dataset by eliminating the features which are not required for the model construction. Feature selection does not totally eliminate an attribute which is considered for the model, rather it mutes that particular characteristic and works with the features which affects the model.Feature selection method aids your mission to create an accurate predictive model. It helps you by choosing features that will give you as good or better accuracy whilst requiring less data. Feature selection methods can be used to identify and remove unnecessary, irrelevant and redundant attributes from the data that do not contribute to the accuracy of the model or may even decrease the accuracy of the model. Having fewer attributes is desirable because it reduces the complexity of the model, and a simpler model is easier to understand, explain and to work with.Feature Selection Algorithms:Filter Method: This method involves assigning scores to individual features and ranking them. The features that have very little to almost no impact are removed from consideration while constructing the model.Wrapper Method: Wrapper method is quite similar to Filter method except the fact that it considers attributes in a group i.e. a number of attributes are taken and checked whether they are having an impact on the model and if not another combination is applied.Embedded Method: Embedded method is the best and most accurate of all the algorithms. It learns the features that affect the model while the model is being constructed and takes into consideration only those features. The most common type of embedded feature selection methods are regularization methods.Cost FunctionCost function helps to figure out the best possible plots which can be used to draw the line of best fit for the data points. As we want to reduce the error of the resulting value we change the process of finding out the actual result to a process which can reduce the error between the predicted value and the actual value.Here, J is the cost function.The above function is made in this format to calculate the error difference between the predicted values and the plotted values. We take the square of the summation of all the data points and divide it by the total number of data points. This cost function J is also called the Mean Squared Error (MSE) function. Using this MSE function we are going to predict values such that the MSE value settles at the minima, reducing the cost function.Gradient DescentGradient Descent is an optimization algorithm that helps machine learning models to find out paths to a minimum value using repeated steps. Gradient descent is used to minimize a function so that it gives the lowest output of that function. This function is called the Loss Function. The loss function shows us how much error is produced by the machine learning model compared to actual results. Our aim should be to lower the cost function as much as possible. One way of achieving a low cost function is by the process of gradient descent. Complexity of some equations makes it difficult to use, partial derivative of the cost function with respect to the considered parameter can provide optimal coefficient value. You may refer to the article on Gradient Descent for Machine Learning.Simple Linear RegressionOptimization is a big part of machine learning and almost every machine learning algorithm has an optimization technique at its core for increased efficiency. Gradient Descent is such an optimization algorithm used to find values of coefficients of a function that minimizes the cost function. Gradient Descent is best applied when the solution cannot be obtained by analytical methods (linear algebra) and must be obtained by an optimization technique.Residual Analysis: Simple linear regression models the relationship between the magnitude of one variable and that of a second—for example, as x increases, y also increases. Or as x increases, y decreases. Correlation is another way to measure how two variables are related. The models done by simple linear regression estimate or try to predict the actual result but most often they deviate from the actual result. Residual analysis is used to calculate by how much the estimated value has deviated from the actual result.Null Hypothesis and p-value: During feature selection, null hypothesis is used to find which attributes will not affect the result of the model. Hypothesis tests are used to test the validity of a claim that is made about a particular attribute of the model. This claim that’s on trial, in essence, is called the null hypothesis. A p-value helps to determine the significance of the results. p-value is a number between 0 and 1 and is interpreted in the following way:A small p-value (less than 0.05) indicates a strong evidence against the null hypothesis, so the null hypothesis is to be rejected.A large p-value (greater than 0.05) indicates weak evidence against the null hypothesis, so the null hypothesis is to be considered.p-value very close to the cut-off (equal to 0.05) is considered to be marginal (could go either way). In this case, the p-value should be provided to the readers so that they can draw their own conclusions.Ordinary Least SquareOrdinary Least Squares (OLS), also known as Ordinary least squares regression or least squared errors regression is a type of linear least squares method for estimating the unknown parameters in a linear regression model. OLS chooses the parameters for a linear function, the goal of which is to minimize the sum of the squares of the difference of the observed variables and the dependent variables i.e. it tries to attain a relationship between them. There are two types of relationships that may occur: linear and curvilinear. A linear relationship is a straight line that is drawn through the central tendency of the points; whereas a curvilinear relationship is a curved line. Association between the variables are depicted by using a scatter plot. The relationship could be positive or negative, and result variation also differs in strength.The advantage of using Ordinary Least Squares regression is that it can be easily interpreted and is highly compatible with recent computers’ built-in algorithms from linear algebra. It can be used to apply to problems with lots of independent variables which can efficiently conveyed to thousands of data points. In Linear Regression, OLS is used to estimate the unknown parameters by creating a model which will minimize the sum of the squared errors between the observed data and the predicted one.Let us simulate some data and look at how the predicted values (Yₑ) differ from the actual value (Y):import pandas as pd import numpy as np from matplotlib import pyplot as plt # Generate 'random' data np.random.seed(0) X = 2.5 * np.random.randn(100) + 1.5   # Array of 100 values with mean = 1.5, stddev = 2.5 res = 0.5 * np.random.randn(100)         # Generate 100 residual terms y = 2 + 0.3 * X + res                   # Actual values of Y # Create pandas dataframe to store our X and y values df = pd.DataFrame(     {'X': X,       'y': y} ) # Show the first five rows of our dataframe df.head()XY05.9101314.71461512.5003932.07623823.9468452.54881137.1022334.61536846.1688953.264107To estimate y using the OLS method, we need to calculate xmean and ymean, the covariance of X and y (xycov), and the variance of X (xvar) before we can determine the values for alpha and beta.# Calculate the mean of X and y xmean = np.mean(X) ymean = np.mean(y) # Calculate the terms needed for the numator and denominator of beta df['xycov'] = (df['X'] - xmean) * (df['y'] - ymean) df['xvar'] = (df['X'] - xmean)**2 # Calculate beta and alpha beta = df['xycov'].sum() / df['xvar'].sum() alpha = ymean - (beta * xmean) print(f'alpha = {alpha}') print(f'beta = {beta}')alpha = 2.0031670124623426 beta = 0.3229396867092763Now that we have an estimate for alpha and beta, we can write our model as Yₑ = 2.003 + 0.323 X, and make predictions:ypred = alpha + beta * XLet’s plot our prediction ypred against the actual values of y, to get a better visual understanding of our model.# Plot regression against actual data plt.figure(figsize=(12, 6)) plt.plot(X, ypred) # regression line plt.plot(X, y, 'ro')   # scatter plot showing actual data plt.title('Actual vs Predicted') plt.xlabel('X') plt.ylabel('y') plt.show()The blue line in the above graph is our line of best fit, Yₑ = 2.003 + 0.323 X.  If you observe the graph carefully, you will notice that there is a linear relationship between X and Y. Using this model, we can predict Y from any values of X. For example, for X = 8,Yₑ = 2.003 + 0.323 (8) = 4.587RegularizationRegularization is a type of regression that is used to decrease the coefficient estimates down to zero. This helps to eliminate the data points that don’t actually represent the true properties of the model, but have appeared by random chance. The process is done by identifying the points which have deviated from the line of best-fit by a large extent. Earlier we saw that to estimate the regression coefficients β in the least squares method, we must minimize the term Residual Sum of Squares (RSS). Let the RSS equation in this case be:The general linear regression model can be expressed using a condensed formula:Here, β=[β0 ,β1, ….. βp]The RSS value will adjust the coefficient, β based on the training data. If the resulting data deviates too much from the training data, then the estimated coefficients won’t generalize well to the future data. This is where regularization comes in and shrinks or regularizes these learned estimates towards zero.Ridge regressionRidge regression is very similar to least squares, except that the Ridge coefficients are estimated by minimizing a different quantity. In particular, the Ridge regression coefficients β are the values that minimize the following quantity:Here, λ is the tuning parameter that decides how much we want to penalize the flexibility of the model. λ controls the relative impact of the two components: RSS and the penalty term. If λ = 0, the Ridge regression will produce a result similar to least squares method. If λ → ∞, all estimated coefficients tend to zero. Ridge regression produces different estimates for different values of λ. The optimal choice of λ is crucial and should be done with cross-validation. The coefficient estimates produced by ridge regression method is also known as the L2 norm.The coefficients generated by Ordinary Least Squares method is independent of scale, which means that if each input variable is multiplied by a constant, the corresponding coefficient will be divided by the same constant, as a result of which the multiplication of the coefficient and the input variables will remain the same. The same is not true for ridge regression and we need to bring the coefficients to the same scale before we perform the process. To standardize the variables, we must subtract their means and divide it by their standard deviations.Lasso RegressionLeast Absolute Shrinkage and Selection Operator (LASSO) regression also shrinks the coefficients by adding a penalty to the sum of squares of the residuals, but the lasso penalty has a slightly different effect. The lasso penalty is the sum of the absolute values of the coefficient vector, which corresponds to its L1 norm. Hence, the lasso estimate is defined by:Similar to ridge regression, the input variables need to be standardized. The lasso penalty makes the solution nonlinear, and there is no closed-form expression for the coefficients as in ridge regression. Instead, the lasso solution is a quadratic programming problem and there are available efficient algorithms that compute the entire path of coefficients that result for different values of λ with the same computational cost as for ridge regression.The lasso penalty had the effect of gradually reducing some coefficients to zero as the regularization increases. For this reason, the lasso can be used for the continuous selection of a subset of features.Linear Regression with multiple variablesLinear regression with multiple variables is also known as "multivariate linear regression". We now introduce notation for equations where we can have any number of input variables.x(i)j=value of feature j in the ith training examplex(i)=the input (features) of the ith training examplem=the number of training examplesn=the number of featuresThe multivariable form of the hypothesis function accommodating these multiple features is as follows:hθ(x)=θ0+θ1x1+θ2x2+θ3x3+⋯+θnxnIn order to develop intuition about this function, we can think about θ0 as the basic price of a house, θ1 as the price per square meter, θ2 as the price per floor, etc. x1 will be the number of square meters in the house, x2 the number of floors, etc.Using the definition of matrix multiplication, our multivariable hypothesis function can be concisely represented as:This is a vectorization of our hypothesis function for one training example; see the lessons on vectorization to learn more.Remark: Note that for convenience reasons in this course we assume x0 (i) =1 for (i∈1,…,m). This allows us to do matrix operations with θ and x. Hence making the two vectors ‘θ’and x(i) match each other element-wise (that is, have the same number of elements: n+1).Multiple Linear RegressionHow is it different?In simple linear regression we use a single independent variable to predict the value of a dependent variable whereas in multiple linear regression two or more independent variables are used to predict the value of a dependent variable. The difference between the two is the number of independent variables. In both cases there is only a single dependent variable.MulticollinearityMulticollinearity tells us the strength of the relationship between independent variables. Multicollinearity is a state of very high intercorrelations or inter-associations among the independent variables. It is therefore a type of disturbance in the data, and if present in the data the statistical inferences made about the data may not be reliable. VIF (Variance Inflation Factor) is used to identify the Multicollinearity. If VIF value is greater than 4, we exclude that variable from our model.There are certain reasons why multicollinearity occurs:It is caused by an inaccurate use of dummy variables.It is caused by the inclusion of a variable which is computed from other variables in the data set.Multicollinearity can also result from the repetition of the same kind of variable.Generally occurs when the variables are highly correlated to each other.Multicollinearity can result in several problems. These problems are as follows:The partial regression coefficient due to multicollinearity may not be estimated precisely. The standard errors are likely to be high.Multicollinearity results in a change in the signs as well as in the magnitudes of the partial regression coefficients from one sample to another sample.Multicollinearity makes it tedious to assess the relative importance of the independent variables in explaining the variation caused by the dependent variable.Iterative ModelsModels should be tested and upgraded again and again for better performance. Multiple iterations allows the model to learn from its previous result and take that into consideration while performing the task again.Making predictions with Linear RegressionLinear Regression can be used to predict the value of an unknown variable using a known variable by the help of a straight line (also called the regression line). The prediction can only be made if it is found that there is a significant correlation between the known and the unknown variable through both a correlation coefficient and a scatterplot.The general procedure for using regression to make good predictions is the following:Research the subject-area so that the model can be built based on the results produced by similar models. This research helps with the subsequent steps.Collect data for appropriate variables which have some correlation with the model.Specify and assess the regression model.Run repeated tests so that the model has more data to work with.To test if the model is good enough observe whether:The scatter plot forms a linear pattern.The correlation coefficient r, has a value above 0.5 or below -0.5. A positive value indicates a positive relationship and a negative value represents a negative relationship.If the correlation coefficient shows a strong relationship between variables but the scatter plot is not linear, the results can be misleading. Examples on how to use linear regression have been shown earlier.Data preparation for Linear RegressionStep 1: Linear AssumptionThe first step for data preparation is checking for the variables which have some sort of linear correlation between the dependent and the independent variables.Step 2: Remove NoiseIt is the process of reducing the number of attributes in the dataset by eliminating the features which have very little to no requirement for the construction of the model.Step 3: Remove CollinearityCollinearity tells us the strength of the relationship between independent variables. If two or more variables are highly collinear, it would not make sense to keep both the variables while evaluating the model and hence we can keep one of them.Step 4: Gaussian DistributionsThe linear regression model will produce more reliable results if the input and output variables have a Gaussian distribution. The Gaussian theorem states that  states that a sample mean from an infinite population is approximately normal, or Gaussian, with mean the same as the underlying population, and variance equal to the population variance divided by the sample size. The approximation improves as the sample size gets large.Step 5: Rescale InputsLinear regression model will produce more reliable predictions if the input variables are rescaled using standardization or normalization.Linear Regression with statsmodelsWe have already discussed OLS method, now we will move on and see how to use the OLS method in the statsmodels library. For this we will be using the popular advertising dataset. Here, we will only be looking at the TV variable and explore whether spending on TV advertising can predict the number of sales for the product. Let’s start by importing this csv file as a pandas dataframe using read_csv():# Import and display first five rows of advertising dataset advert = pd.read_csv('advertising.csv') advert.head()TVRadioNewspaperSales0230.137.869.222.1144.539.345.110.4217.245.969.312.03151.541.358.516.54180.810.858.417.9Now we will use statsmodels’ OLS function to initialize simple linear regression model. It will take the formula y ~ X, where X is the predictor variable (TV advertising costs) and y is the output variable (Sales). Then, we will fit the model by calling the OLS object’s fit() method.import statsmodels.formula.api as smf # Initialise and fit linear regression model using `statsmodels` model = smf.ols('Sales ~ TV', data=advert) model = model.fit()Once we have fit the simple regression model, we can predict the values of sales based on the equation we just derived using the .predict method and also visualise our regression model by plotting sales_pred against the TV advertising costs to find the line of best fit.# Predict values sales_pred = model.predict() # Plot regression against actual data plt.figure(figsize=(12, 6)) plt.plot(advert['TV'], advert['Sales'], 'o')       # scatter plot showing actual data plt.plot(advert['TV'], sales_pred, 'r', linewidth=2)   # regression line plt.xlabel('TV Advertising Costs') plt.ylabel('Sales') plt.title('TV vs Sales') plt.show()In the above graph, if you notice you will see that there is a positive linear relationship between TV advertising costs and Sales. You may also summarize by saying that spending more on TV advertising predicts a higher number of sales.Linear Regression with scikit-learnLet us learn to implement linear regression models using sklearn. For this model as well, we will continue to use the advertising dataset but now we will use two predictor variables to create a multiple linear regression model. Yₑ = α + β₁X₁ + β₂X₂ + … + βₚXₚ, where p is the number of predictors.In our example, we will be predicting Sales using the variables TV and Radio i.e. our model can be written as:Sales = α + β₁*TV + β₂*Radiofrom sklearn.linear_model import LinearRegression # Build linear regression model using TV and Radio as predictors # Split data into predictors X and output Y predictors = ['TV', 'Radio'] X = advert[predictors] y = advert['Sales'] # Initialise and fit model lm = LinearRegression() model = lm.fit(X, y) print(f'alpha = {model.intercept_}') print(f'betas = {model.coef_}')alpha = 4.630879464097768 betas = [0.05444896 0.10717457]model.predict(X)Now that we have fit a multiple linear regression model to our data, we can predict sales from any combination of TV and Radio advertising costs. For example, you want to know how many sales we would make if we invested $600 in TV advertising and $300 in Radio advertising. You can simply find it out by:new_X = [[600, 300]] print(model.predict(new_X))[69.4526273]We get the output as 69.45 which means if we invest $600 on TV and $300 on Radio advertising, we can expect to sell 69 units approximately.SummaryLet us sum up what we have covered in this article so far —How to understand a regression problemWhat is linear regression and how it worksOrdinary Least Square method and RegularizationImplementing Linear Regression in Python using statsmodel and sklearn libraryWe have discussed about a couple of ways to implement linear regression and build efficient models for certain business problems. If you are inspired by the opportunities provided by machine learning, enrol in our  Data Science and Machine Learning Courses for more lucrative career options in this landscape.

What is Linear Regression in Machine Learning

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What is Linear Regression in Machine Learning

Machine Learning, being a subset of Artificial Intelligence (AI), has been playing a dominant role in our daily lives. Data science engineers and developers working in various domains are widely using machine learning algorithms to make their tasks simpler and life easier. For example, certain machine learning algorithms enable Google Maps to find the fastest route to our destinations, allow Tesla to make driverless cars, help Amazon to generate almost 35% of their annual income, AccuWeather to get the weather forecast of 3.5 million locations weeks in advance, Facebook to automatically detect faces and suggest tags and so on.

In statistics and machine learning, linear regression is one of the most popular and well understood algorithms. Most data science enthusiasts and machine learning  fanatics begin their journey with linear regression algorithms. In this article, we will look into how linear regression algorithm works and how it can be efficiently used in your machine learning projects to build better models.

Linear Regression is one of the machine learning algorithms where the result is predicted by the use of known parameters which are correlated with the output. It is used to predict values within a continuous range rather than trying to classify them into categories. The known parameters are used to make a continuous and constant slope which is used to predict the unknown or the result.

What is a Regression Problem?

Majority of the machine learning algorithms fall under the supervised learning category. It is the process where an algorithm is used to predict a result based on the previously entered values and the results generated from them. Suppose we have an input variable ‘x’ and an output variable ‘y’ where y is a function of x (y=f{x}). Supervised learning reads the value of entered variable ‘x’ and the resulting variable ‘y’ so that it can use those results to later predict a highly accurate output data of ‘y’ from the entered value of ‘x’. A regression problem is when the resulting variable contains a real or a continuous value. It tries to draw the line of best fit from the data gathered from a number of points.

What is a Regression Problem?

For example, which of these is a regression problem?

  • How much gas will I spend if I drive for 100 miles?
  • What is the nationality of a person?
  • What is the age of a person?
  • Which is the closest planet to the Sun?

Predicting the amount of gas to be spent and the age of a person are regression problems. Predicting nationality is categorical and the closest planet to the Sun is discrete.

What is Linear Regression?

Let’s say we have a dataset which contains information about the relationship between ‘number of hours studied’ and ‘marks obtained’. A number of students have been observed and their hours of study along with their grades are recorded. This will be our training data. Our goal is to design a model that can predict the marks if number of hours studied is provided. Using the training data, a regression line is obtained which will give minimum error. This linear equation is then used to apply for a new data. That is, if we give the number of hours studied by a student as an input, our model should be able to predict their mark with minimum error.

Hypothesis of Linear Regression

The linear regression model can be represented by the following equation:

The linear regression model equation

where,

Y is the predicted value

θ₀ is the bias term.

θ₁,…,θn are the model parameters

x₁, x₂,…,xn are the feature values.

The above hypothesis can also be represented by

The above hypothesis

Where, θ is the model’s parameter vector including the bias term θ₀; x is the feature vector with x₀ =1

Y (pred) = b0 + b1*x

The values b0 and b1 must be chosen so that the error is minimum. If sum of squared error is taken as a metric to evaluate the model, then the goal is to obtain a line that best reduces the error.

Error Calculation in Linear Regression

If we don’t square the error, then the positive and negative points will cancel each other out.

For a model with one predictor,

Intercept Calculation in Linear Regression

Coefficient Formula in Linear Regression

Exploring ‘b1

If b1 > 0, then x (predictor) and y(target) have a positive relationship. That is an increase in x will increase y.

If b1 < 0, then x (predictor) and y(target) have a negative relationship. That is an increase in x will decrease y.

Exploring ‘b0

If the model does not include x=0, then the prediction will become meaningless with only b0. For example, we have a dataset that relates height(x) and weight(y). Taking x=0 (that is height as 0), will make the equation have only b0 value which is completely meaningless as in real-time height and weight can never be zero. This resulted due to considering the model values beyond its scope.

If the model includes value 0, then ‘b0’ will be the average of all predicted values when x=0. But, setting zero for all the predictor variables is often impossible.

The value of b0 guarantees that the residual will have mean zero. If there is no ‘b0’ term, then the regression will be forced to pass over the origin. Both the regression coefficient and prediction will be biased.

How does Linear Regression work?

Let’s look at a scenario where linear regression might be useful: losing weight. Let us consider that there’s a connection between how many calories you take in and how much you weigh; regression analysis can help you understand that connection. Regression analysis will provide you with a relation which can be visualized into a graph in order to make predictions about your data. For example, if you’ve been putting on weight over the last few years, it can predict how much you’ll weigh in the next ten years if you continue to consume the same amount of calories and burn them at the same rate.

The goal of regression analysis is to create a trend line based on the data you have gathered. This then allows you to determine whether other factors apart from the amount of calories consumed affect your weight, such as the number of hours you sleep, work pressure, level of stress, type of exercises you do etc. Before taking into account, we need to look at these factors and attributes and determine whether there is a correlation between them. Linear Regression can then be used to draw a trend line which can then be used to confirm or deny the relationship between attributes. If the test is done over a long time duration, extensive data can be collected and the result can be evaluated more accurately. By the end of this article we will build a model which looks like the below picture i.e, determine a line which best fits the data.

How does Linear Regression work?

How do we determine the best fit line?

The best fit line is considered to be the line for which the error between the predicted values and the observed values is minimum. It is also called the regression line and the errors are also known as residuals. The figure shown below shows the residuals. It can be visualized by the vertical lines from the observed data value to the regression line.

How do we determine the best fit line?

When to use Linear Regression?

Linear Regression’s power lies in its simplicity, which means that it can be used to solve problems across various fields. At first, the data collected from the observations need to be collected and plotted along a line. If the difference between the predicted value and the result is almost the same, we can use linear regression for the problem.

Assumptions in linear regression

If you are planning to use linear regression for your problem then there are some assumptions you need to consider:

  • The relation between the dependent and independent variables should be almost linear.
  • The data is homoscedastic, meaning the variance between the results should not be too much.
  • The results obtained from an observation should not be influenced by the results obtained from the previous observation.
  • The residuals should be normally distributed. This assumption means that the probability density function of the residual values is normally distributed at each independent value.

You can determine whether your data meets these conditions by plotting it and then doing a bit of digging into its structure.

Few properties of Regression Line

Here are a few features a regression line has:

  • Regression passes through the mean of independent variable (x) as well as mean of the dependent variable (y).
  • Regression line minimizes the sum of “Square of Residuals”. That’s why the method of Linear Regression is known as “Ordinary Least Square (OLS)”. We will discuss more in detail about Ordinary Least Square later on.
  • B1 explains the change in Y with a change in x  by one unit. In other words, if we increase the value of ‘x’ it will result in a change in value of Y.

Finding a Linear Regression line

Let’s say we want to predict ‘y’ from ‘x’ given in the following table and assume they are correlated as “y=B0+B1∗x”

xyPredicted 'y'
12Β0+B1∗1
21Β0+B1∗2
33Β0+B1∗3
46Β0+B1∗4
59Β0+B1∗5
611Β0+B1∗6
713Β0+B1∗7
815Β0+B1∗8
917Β0+B1∗9
1020Β0+B1∗10

where,

Std. Dev. of x3.02765
Std. Dev. of y6.617317
Mean of x5.5
Mean of y9.7
Correlation between x & y0.989938

If the Residual Sum of Square (RSS) is differentiated with respect to B0 & B1 and the results equated to zero, we get the following equation:

B1 = Correlation * (Std. Dev. of y/ Std. Dev. of x)

B0 = Mean(Y) – B1 * Mean(X)

Putting values from table 1 into the above equations,

B1 = 2.64

B0 = -2.2

Hence, the least regression equation will become –

Y = -2.2 + 2.64*x

xY - ActualY - Predicted
120.44
213.08
335.72
468.36
5911
61113.64
71316.28
81518.92
91721.56
102024.2

As there are only 10 data points, the results are not too accurate but if we see the correlation between the predicted and actual line, it has turned out to be very high; both the lines are moving almost together and here is the graph for visualizing our predicted values:

Finding a Linear Regression line

Model Performance

After the model is built, if we see that the difference in the values of the predicted and actual data is not much, it is considered to be a good model and can be used to make future predictions. The amount that we consider “not much” entirely depends on the task you want to perform and to what percentage the variation in data can be handled. Here are a few metric tools we can use to calculate error in the model-

R – Square (R2)

Model Performance

Total Sum of Squares (TSS): total sum of squares (TSS) is a quantity that appears as part of a standard way of presenting results of such an analysis. Sum of squares is a measure of how a data set varies around a central number (like the mean). The Total Sum of Squares tells how much variation there is in the dependent variable.

TSS = Σ (Y – Mean[Y])2

Residual Sum of Squares (RSS): The residual sum of squares tells you how much of the dependent variable’s variation your model did not explain. It is the sum of the squared differences between the actual Y and the predicted Y.

RSS = Σ (Y – f[Y])2

(TSS – RSS) measures the amount of variability in the response that is explained by performing the regression.

Properties of R2

  • R2 always ranges between 0 to 1.
  • R2 of 0 means that there is no correlation between the dependent and the independent variable.
  • R2 of 1 means the dependent variable can be predicted from the independent variable without any error. 
  • An R2 between 0 and 1 indicates the extent to which the dependent variable is predictable. An R2 of 0.20 means that there is 20% of the variance in Y is predictable from X; an R2 of 0.40 means that 40% is predictable; and so on.

Root Mean Square Error (RMSE)

Root Mean Square Error (RMSE) is the standard deviation of the residuals (prediction errors). The formula for calculating RMSE is:

Root Mean Square Error (RMSE)

Where N : Total number of observations

When standardized observations are used as RMSE inputs, there is a direct relationship with the correlation coefficient. For example, if the correlation coefficient is 1, the RMSE will be 0, because all of the points lie on the regression line (and therefore there are no errors).

Mean Absolute Percentage Error (MAPE)

There are certain limitations to the use of RMSE, so analysts prefer MAPE over RMSE which gives error in terms of percentages so that different models can be considered for the task and see how they perform. Formula for calculating MAPE can be written as:

Mean Absolute Percentage Error (MAPE)

Where N : Total number of observations

Feature Selection

Feature selection is the automatic selection of attributes for your data that are most relevant to the predictive model you are working on. It seeks to reduce the number of attributes in the dataset by eliminating the features which are not required for the model construction. Feature selection does not totally eliminate an attribute which is considered for the model, rather it mutes that particular characteristic and works with the features which affects the model.

Feature selection method aids your mission to create an accurate predictive model. It helps you by choosing features that will give you as good or better accuracy whilst requiring less data. Feature selection methods can be used to identify and remove unnecessary, irrelevant and redundant attributes from the data that do not contribute to the accuracy of the model or may even decrease the accuracy of the model. Having fewer attributes is desirable because it reduces the complexity of the model, and a simpler model is easier to understand, explain and to work with.

Feature Selection Algorithms:

  • Filter Method: This method involves assigning scores to individual features and ranking them. The features that have very little to almost no impact are removed from consideration while constructing the model.
  • Wrapper Method: Wrapper method is quite similar to Filter method except the fact that it considers attributes in a group i.e. a number of attributes are taken and checked whether they are having an impact on the model and if not another combination is applied.
  • Embedded Method: Embedded method is the best and most accurate of all the algorithms. It learns the features that affect the model while the model is being constructed and takes into consideration only those features. The most common type of embedded feature selection methods are regularization methods.

Cost Function

Cost function helps to figure out the best possible plots which can be used to draw the line of best fit for the data points. As we want to reduce the error of the resulting value we change the process of finding out the actual result to a process which can reduce the error between the predicted value and the actual value.

Cost Function in Linear Regression

Here, J is the cost function.

The above function is made in this format to calculate the error difference between the predicted values and the plotted values. We take the square of the summation of all the data points and divide it by the total number of data points. This cost function J is also called the Mean Squared Error (MSE) function. Using this MSE function we are going to predict values such that the MSE value settles at the minima, reducing the cost function.

Gradient Descent

Gradient Descent is an optimization algorithm that helps machine learning models to find out paths to a minimum value using repeated steps. Gradient descent is used to minimize a function so that it gives the lowest output of that function. This function is called the Loss Function. The loss function shows us how much error is produced by the machine learning model compared to actual results. Our aim should be to lower the cost function as much as possible. One way of achieving a low cost function is by the process of gradient descent. Complexity of some equations makes it difficult to use, partial derivative of the cost function with respect to the considered parameter can provide optimal coefficient value. You may refer to the article on Gradient Descent for Machine Learning.

Simple Linear Regression

Optimization is a big part of machine learning and almost every machine learning algorithm has an optimization technique at its core for increased efficiency. Gradient Descent is such an optimization algorithm used to find values of coefficients of a function that minimizes the cost function. Gradient Descent is best applied when the solution cannot be obtained by analytical methods (linear algebra) and must be obtained by an optimization technique.

Residual Analysis: Simple linear regression models the relationship between the magnitude of one variable and that of a second—for example, as x increases, y also increases. Or as x increases, y decreases. Correlation is another way to measure how two variables are related. The models done by simple linear regression estimate or try to predict the actual result but most often they deviate from the actual result. Residual analysis is used to calculate by how much the estimated value has deviated from the actual result.

Null Hypothesis and p-value: During feature selection, null hypothesis is used to find which attributes will not affect the result of the model. Hypothesis tests are used to test the validity of a claim that is made about a particular attribute of the model. This claim that’s on trial, in essence, is called the null hypothesis. A p-value helps to determine the significance of the results. p-value is a number between 0 and 1 and is interpreted in the following way:

  • A small p-value (less than 0.05) indicates a strong evidence against the null hypothesis, so the null hypothesis is to be rejected.
  • A large p-value (greater than 0.05) indicates weak evidence against the null hypothesis, so the null hypothesis is to be considered.
  • p-value very close to the cut-off (equal to 0.05) is considered to be marginal (could go either way). In this case, the p-value should be provided to the readers so that they can draw their own conclusions.

Ordinary Least Square

Ordinary Least Squares (OLS), also known as Ordinary least squares regression or least squared errors regression is a type of linear least squares method for estimating the unknown parameters in a linear regression model. OLS chooses the parameters for a linear function, the goal of which is to minimize the sum of the squares of the difference of the observed variables and the dependent variables i.e. it tries to attain a relationship between them. 

There are two types of relationships that may occur: linear and curvilinear. A linear relationship is a straight line that is drawn through the central tendency of the points; whereas a curvilinear relationship is a curved line. Association between the variables are depicted by using a scatter plot. The relationship could be positive or negative, and result variation also differs in strength.

The advantage of using Ordinary Least Squares regression is that it can be easily interpreted and is highly compatible with recent computers’ built-in algorithms from linear algebra. It can be used to apply to problems with lots of independent variables which can efficiently conveyed to thousands of data points. In Linear Regression, OLS is used to estimate the unknown parameters by creating a model which will minimize the sum of the squared errors between the observed data and the predicted one.

Let us simulate some data and look at how the predicted values (Yₑ) differ from the actual value (Y):

import pandas as pd
import numpy as np
from matplotlib import pyplot as plt

# Generate 'random' data
np.random.seed(0)
X = 2.5 * np.random.randn(100) + 1.5         # Array of 100 values with mean = 1.5, stddev = 2.5
res = 0.5 * np.random.randn(100)         # Generate 100 residual terms
y = 2 + 0.3 * X + res                    # Actual values of Y

# Create pandas dataframe to store our X and y values
df = pd.DataFrame(
    {'X': X,
      'y': y}
)

# Show the first five rows of our dataframe
df.head()

XY
05.9101314.714615
12.5003932.076238
23.9468452.548811
37.1022334.615368
46.1688953.264107

To estimate y using the OLS method, we need to calculate xmean and ymean, the covariance of X and y (xycov), and the variance of X (xvar) before we can determine the values for alpha and beta.

# Calculate the mean of X and y
xmean = np.mean(X)
ymean = np.mean(y)

# Calculate the terms needed for the numator and denominator of beta
df['xycov'] = (df['X'] - xmean) * (df['y'] - ymean)
df['xvar'] = (df['X'] - xmean)**2

# Calculate beta and alpha
beta = df['xycov'].sum() / df['xvar'].sum()
alpha = ymean - (beta * xmean)
print(f'alpha = {alpha}')
print(f'beta = {beta}')
alpha = 2.0031670124623426
beta = 0.3229396867092763

Now that we have an estimate for alpha and beta, we can write our model as Yₑ = 2.003 + 0.323 X, and make predictions:

ypred = alpha + beta * X

Let’s plot our prediction ypred against the actual values of y, to get a better visual understanding of our model.

# Plot regression against actual data
plt.figure(figsize=(12, 6))
plt.plot(X, ypred) # regression line
plt.plot(X, y, 'ro')   # scatter plot showing actual data
plt.title('Actual vs Predicted')
plt.xlabel('X')
plt.ylabel('y')

plt.show()

The blue line in the above graph is our line of best fit

The blue line in the above graph is our line of best fit, Yₑ = 2.003 + 0.323 X.  If you observe the graph carefully, you will notice that there is a linear relationship between X and Y. Using this model, we can predict Y from any values of X. For example, for X = 8,

Yₑ = 2.003 + 0.323 (8) = 4.587

Regularization

Regularization is a type of regression that is used to decrease the coefficient estimates down to zero. This helps to eliminate the data points that don’t actually represent the true properties of the model, but have appeared by random chance. The process is done by identifying the points which have deviated from the line of best-fit by a large extent. Earlier we saw that to estimate the regression coefficients β in the least squares method, we must minimize the term Residual Sum of Squares (RSS). Let the RSS equation in this case be:

Regularization in Linear Regression

The general linear regression model can be expressed using a condensed formula:

expressed using a condensed formula

Here, β=[β01, ….. βp]

The RSS value will adjust the coefficient, β based on the training data. If the resulting data deviates too much from the training data, then the estimated coefficients won’t generalize well to the future data. This is where regularization comes in and shrinks or regularizes these learned estimates towards zero.

Ridge regression

Ridge regression is very similar to least squares, except that the Ridge coefficients are estimated by minimizing a different quantity. In particular, the Ridge regression coefficients β are the values that minimize the following quantity:

Ridge regression in Linear Regression

Here, λ is the tuning parameter that decides how much we want to penalize the flexibility of the model. λ controls the relative impact of the two components: RSS and the penalty term. If λ = 0, the Ridge regression will produce a result similar to least squares method. If λ → ∞, all estimated coefficients tend to zero. Ridge regression produces different estimates for different values of λ. The optimal choice of λ is crucial and should be done with cross-validation. The coefficient estimates produced by ridge regression method is also known as the L2 norm.

The coefficients generated by Ordinary Least Squares method is independent of scale, which means that if each input variable is multiplied by a constant, the corresponding coefficient will be divided by the same constant, as a result of which the multiplication of the coefficient and the input variables will remain the same. The same is not true for ridge regression and we need to bring the coefficients to the same scale before we perform the process. To standardize the variables, we must subtract their means and divide it by their standard deviations.

Lasso Regression

Least Absolute Shrinkage and Selection Operator (LASSO) regression also shrinks the coefficients by adding a penalty to the sum of squares of the residuals, but the lasso penalty has a slightly different effect. The lasso penalty is the sum of the absolute values of the coefficient vector, which corresponds to its L1 norm. Hence, the lasso estimate is defined by:

Lasso Regression in Linear Regression

Similar to ridge regression, the input variables need to be standardized. The lasso penalty makes the solution nonlinear, and there is no closed-form expression for the coefficients as in ridge regression. Instead, the lasso solution is a quadratic programming problem and there are available efficient algorithms that compute the entire path of coefficients that result for different values of λ with the same computational cost as for ridge regression.

The lasso penalty had the effect of gradually reducing some coefficients to zero as the regularization increases. For this reason, the lasso can be used for the continuous selection of a subset of features.

Linear Regression with multiple variables

Linear regression with multiple variables is also known as "multivariate linear regression". We now introduce notation for equations where we can have any number of input variables.

x(i)j=value of feature j in the ith training example

x(i)=the input (features) of the ith training example

m=the number of training examples

n=the number of features

The multivariable form of the hypothesis function accommodating these multiple features is as follows:

hθ(x)=θ01x12x23x3+⋯+θnxn

In order to develop intuition about this function, we can think about θ0 as the basic price of a house, θ1 as the price per square meter, θ2 as the price per floor, etc. x1 will be the number of square meters in the house, x2 the number of floors, etc.

Using the definition of matrix multiplication, our multivariable hypothesis function can be concisely represented as:

Linear Regression with multiple variables

This is a vectorization of our hypothesis function for one training example; see the lessons on vectorization to learn more.

Remark: Note that for convenience reasons in this course we assume x0 (i) =1 for (i∈1,…,m). This allows us to do matrix operations with θ and x. Hence making the two vectors ‘θ’and x(i) match each other element-wise (that is, have the same number of elements: n+1).

Multiple Linear Regression

How is it different?

In simple linear regression we use a single independent variable to predict the value of a dependent variable whereas in multiple linear regression two or more independent variables are used to predict the value of a dependent variable. The difference between the two is the number of independent variables. In both cases there is only a single dependent variable.

Multicollinearity

Multicollinearity tells us the strength of the relationship between independent variables. Multicollinearity is a state of very high intercorrelations or inter-associations among the independent variables. It is therefore a type of disturbance in the data, and if present in the data the statistical inferences made about the data may not be reliable. VIF (Variance Inflation Factor) is used to identify the Multicollinearity. If VIF value is greater than 4, we exclude that variable from our model.

There are certain reasons why multicollinearity occurs:

  • It is caused by an inaccurate use of dummy variables.
  • It is caused by the inclusion of a variable which is computed from other variables in the data set.
  • Multicollinearity can also result from the repetition of the same kind of variable.
  • Generally occurs when the variables are highly correlated to each other.

Multicollinearity can result in several problems. These problems are as follows:

  • The partial regression coefficient due to multicollinearity may not be estimated precisely. The standard errors are likely to be high.
  • Multicollinearity results in a change in the signs as well as in the magnitudes of the partial regression coefficients from one sample to another sample.
  • Multicollinearity makes it tedious to assess the relative importance of the independent variables in explaining the variation caused by the dependent variable.

Iterative Models

Models should be tested and upgraded again and again for better performance. Multiple iterations allows the model to learn from its previous result and take that into consideration while performing the task again.

Making predictions with Linear Regression

Linear Regression can be used to predict the value of an unknown variable using a known variable by the help of a straight line (also called the regression line). The prediction can only be made if it is found that there is a significant correlation between the known and the unknown variable through both a correlation coefficient and a scatterplot.

The general procedure for using regression to make good predictions is the following:

  • Research the subject-area so that the model can be built based on the results produced by similar models. This research helps with the subsequent steps.
  • Collect data for appropriate variables which have some correlation with the model.
  • Specify and assess the regression model.
  • Run repeated tests so that the model has more data to work with.

To test if the model is good enough observe whether:

  • The scatter plot forms a linear pattern.
  • The correlation coefficient r, has a value above 0.5 or below -0.5. A positive value indicates a positive relationship and a negative value represents a negative relationship.

If the correlation coefficient shows a strong relationship between variables but the scatter plot is not linear, the results can be misleading. Examples on how to use linear regression have been shown earlier.

Data preparation for Linear Regression

Step 1: Linear Assumption

The first step for data preparation is checking for the variables which have some sort of linear correlation between the dependent and the independent variables.

Step 2: Remove Noise

It is the process of reducing the number of attributes in the dataset by eliminating the features which have very little to no requirement for the construction of the model.

Step 3: Remove Collinearity

Collinearity tells us the strength of the relationship between independent variables. If two or more variables are highly collinear, it would not make sense to keep both the variables while evaluating the model and hence we can keep one of them.

Step 4: Gaussian Distributions

The linear regression model will produce more reliable results if the input and output variables have a Gaussian distribution. The Gaussian theorem states that  states that a sample mean from an infinite population is approximately normal, or Gaussian, with mean the same as the underlying population, and variance equal to the population variance divided by the sample size. The approximation improves as the sample size gets large.

Step 5: Rescale Inputs

Linear regression model will produce more reliable predictions if the input variables are rescaled using standardization or normalization.

Linear Regression with statsmodels

We have already discussed OLS method, now we will move on and see how to use the OLS method in the statsmodels library. For this we will be using the popular advertising dataset. Here, we will only be looking at the TV variable and explore whether spending on TV advertising can predict the number of sales for the product. Let’s start by importing this csv file as a pandas dataframe using read_csv():

# Import and display first five rows of advertising dataset
advert = pd.read_csv('advertising.csv')
advert.head()

TVRadioNewspaperSales
0230.137.869.222.1
144.539.345.110.4
217.245.969.312.0
3151.541.358.516.5
4180.810.858.417.9

Now we will use statsmodels’ OLS function to initialize simple linear regression model. It will take the formula y ~ X, where X is the predictor variable (TV advertising costs) and y is the output variable (Sales). Then, we will fit the model by calling the OLS object’s fit() method.

import statsmodels.formula.api as smf

# Initialise and fit linear regression model using `statsmodels`
model = smf.ols('Sales ~ TV', data=advert)
model = model.fit()

Once we have fit the simple regression model, we can predict the values of sales based on the equation we just derived using the .predict method and also visualise our regression model by plotting sales_pred against the TV advertising costs to find the line of best fit.

# Predict values
sales_pred = model.predict()

# Plot regression against actual data
plt.figure(figsize=(12, 6))
plt.plot(advert['TV'], advert['Sales'], 'o')       # scatter plot showing actual data
plt.plot(advert['TV'], sales_pred, 'r', linewidth=2)   # regression line
plt.xlabel('TV Advertising Costs')
plt.ylabel('Sales')
plt.title('TV vs Sales')

plt.show()

Linear Regression with statsmodels

In the above graph, if you notice you will see that there is a positive linear relationship between TV advertising costs and Sales. You may also summarize by saying that spending more on TV advertising predicts a higher number of sales.

Linear Regression with scikit-learn

Let us learn to implement linear regression models using sklearn. For this model as well, we will continue to use the advertising dataset but now we will use two predictor variables to create a multiple linear regression model. 

Yₑ = α + β₁X₁ + β₂X₂ + … + βₚXₚ, where p is the number of predictors.

In our example, we will be predicting Sales using the variables TV and Radio i.e. our model can be written as:

Sales = α + β₁*TV + β₂*Radio

from sklearn.linear_model import LinearRegression

# Build linear regression model using TV and Radio as predictors
# Split data into predictors X and output Y
predictors = ['TV', 'Radio']
X = advert[predictors]
y = advert['Sales']

# Initialise and fit model
lm = LinearRegression()
model = lm.fit(X, y)
print(f'alpha = {model.intercept_}')
print(f'betas = {model.coef_}')
alpha = 4.630879464097768
betas = [0.05444896 0.10717457]
model.predict(X)

Linear Regression with scikit-learn

Now that we have fit a multiple linear regression model to our data, we can predict sales from any combination of TV and Radio advertising costs. For example, you want to know how many sales we would make if we invested $600 in TV advertising and $300 in Radio advertising. You can simply find it out by:

new_X = [[600, 300]]
print(model.predict(new_X))
[69.4526273]

We get the output as 69.45 which means if we invest $600 on TV and $300 on Radio advertising, we can expect to sell 69 units approximately.

Summary

Let us sum up what we have covered in this article so far —

  • How to understand a regression problem
  • What is linear regression and how it works
  • Ordinary Least Square method and Regularization
  • Implementing Linear Regression in Python using statsmodel and sklearn library

We have discussed about a couple of ways to implement linear regression and build efficient models for certain business problems. If you are inspired by the opportunities provided by machine learning, enrol in our  Data Science and Machine Learning Courses for more lucrative career options in this landscape.

Priyankur

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.

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Types of Probability Distributions Every Data Science Expert Should know

Data Science has become one of the most popular interdisciplinary fields. It uses scientific approaches, methods, algorithms, and operations to obtain facts and insights from unstructured, semi-structured, and structured datasets. Organizations use these collected facts and insights for efficient production, business growth, and to predict user requirements. Probability distribution plays a significant role in performing data analysis equipping a dataset for training a model. In this article, you will learn about the types of Probability Distribution, random variables, types of discrete distributions, and continuous distribution.  What is Probability Distribution? A Probability Distribution is a statistical method that determines all the probable values and possibilities that a random variable can deliver from a particular range. This range of values will have a lower bound and an upper bound, which we call the minimum and the maximum possible values.  Various factors on which plotting of a value depends are standard deviation, mean (or average), skewness, and kurtosis. All of these play a significant role in Data science as well. We can use probability distribution in physics, engineering, finance, data analysis, machine learning, etc. Significance of Probability distributions in Data Science In a way, most of the data science and machine learning operations are dependent on several assumptions about the probability of your data. Probability distribution allows a skilled data analyst to recognize and comprehend patterns from large data sets; that is, otherwise, entirely random variables and values. Thus, it makes probability distribution a toolkit based on which we can summarize a large data set. The density function and distribution techniques can also help in plotting data, thus supporting data analysts to visualize data and extract meaning. General Properties of Probability Distributions Probability distribution determines the likelihood of any outcome. The mathematical expression takes a specific value of x and shows the possibility of a random variable with p(x). Some general properties of the probability distribution are – The total of all probabilities for any possible value becomes equal to 1. In a probability distribution, the possibility of finding any specific value or a range of values must lie between 0 and 1. Probability distributions tell us the dispersal of the values from the random variable. Consequently, the type of variable also helps determine the type of probability distribution.Common Data Types Before jumping directly into explaining the different probability distributions, let us first understand the different types of probability distributions or the main categories of the probability distribution. Data analysts and data engineers have to deal with a broad spectrum of data, such as text, numerical, image, audio, voice, and many more. Each of these have a specific means to be represented and analyzed. Data in a probability distribution can either be discrete or continuous. Numerical data especially takes one of the two forms. Discrete data: They take specific values where the outcome of the data remains fixed. Like, for example, the consequence of rolling two dice or the number of overs in a T-20 match. In the first case, the result lies between 2 and 12. In the second case, the event will be less than 20. Different types of discrete distributions that use discrete data are: Binomial Distribution Hypergeometric Distribution Geometric Distribution Poisson Distribution Negative Binomial Distribution Multinomial Distribution  Continuous data: It can obtain any value irrespective of bound or limit. Example: weight, height, any trigonometric value, age, etc. Different types of continuous distributions that use continuous data are: Beta distribution Cauchy distribution Exponential distribution Gamma distribution Logistic distribution Weibull distribution Types of Probability Distribution explained Here are some of the popular types of Probability distributions used by data science professionals. (Try all the code using Jupyter Notebook) Normal Distribution: It is also known as Gaussian distribution. It is one of the simplest types of continuous distribution. This probability distribution is symmetrical around its mean value. It also shows that data at close proximity of the mean is frequently occurring, compared to data that is away from it. Here, mean = 0, variance = finite valueHere, you can see 0 at the center is the Normal Distribution for different mean and variance values. Here is a code example showing the use of Normal Distribution: from scipy.stats import norm  import matplotlib.pyplot as mpl  import numpy as np  def normalDist() -> None:      fig, ax = mpl.subplots(1, 1)      mean, var, skew, kurt = norm.stats(moments = 'mvsk')      x = np.linspace(norm.ppf(0.01),  norm.ppf(0.99), 100)      ax.plot(x, norm.pdf(x),          'r-', lw = 5, alpha = 0.6, label = 'norm pdf')      ax.plot(x, norm.cdf(x),          'b-', lw = 5, alpha = 0.6, label = 'norm cdf')      vals = norm.ppf([0.001, 0.5, 0.999])      np.allclose([0.001, 0.5, 0.999], norm.cdf(vals))      r = norm.rvs(size = 1000)      ax.hist(r, normed = True, histtype = 'stepfilled', alpha = 0.2)      ax.legend(loc = 'best', frameon = False)      mpl.show()  normalDist() Output: Bernoulli Distribution: It is the simplest type of probability distribution. It is a particular case of Binomial distribution, where n=1. It means a binomial distribution takes 'n' number of trials, where n > 1 whereas, the Bernoulli distribution takes only a single trial.   Probability Mass Function of a Bernoulli’s Distribution is:  where p = probability of success and q = probability of failureHere is a code example showing the use of Bernoulli Distribution: from scipy.stats import bernoulli  import seaborn as sb    def bernoulliDist():      data_bern = bernoulli.rvs(size=1200, p = 0.7)      ax = sb.distplot(          data_bern,           kde = True,           color = 'g',           hist_kws = {'alpha' : 1},          kde_kws = {'color': 'y', 'lw': 3, 'label': 'KDE'})      ax.set(xlabel = 'Bernouli Values', ylabel = 'Frequency Distribution')  bernoulliDist() Output:Continuous Uniform Distribution: In this type of continuous distribution, all outcomes are equally possible; each variable gets the same probability of hit as a consequence. This symmetric probabilistic distribution has random variables at an equal interval, with the probability of 1/(b-a). Here is a code example showing the use of Uniform Distribution: from numpy import random  import matplotlib.pyplot as mpl  import seaborn as sb  def uniformDist():      sb.distplot(random.uniform(size = 1200), hist = True)      mpl.show()  uniformDist() Output: Log-Normal Distribution: A Log-Normal distribution is another type of continuous distribution of logarithmic values that form a normal distribution. We can transform a log-normal distribution into a normal distribution. Here is a code example showing the use of Log-Normal Distribution import matplotlib.pyplot as mpl  def lognormalDist():      muu, sig = 3, 1      s = np.random.lognormal(muu, sig, 1000)      cnt, bins, ignored = mpl.hist(s, 80, normed = True, align ='mid', color = 'y')      x = np.linspace(min(bins), max(bins), 10000)      calc = (np.exp( -(np.log(x) - muu) **2 / (2 * sig**2))             / (x * sig * np.sqrt(2 * np.pi)))      mpl.plot(x, calc, linewidth = 2.5, color = 'g')      mpl.axis('tight')      mpl.show()  lognormalDist() Output: Pareto Distribution: It is one of the most critical types of continuous distribution. The Pareto Distribution is a skewed statistical distribution that uses power-law to describe quality control, scientific, social, geophysical, actuarial, and many other types of observable phenomena. The distribution shows slow or heavy-decaying tails in the plot, where much of the data reside at its extreme end. Here is a code example showing the use of Pareto Distribution – import numpy as np  from matplotlib import pyplot as plt  from scipy.stats import pareto  def paretoDist():      xm = 1.5        alp = [2, 4, 6]       x = np.linspace(0, 4, 800)      output = np.array([pareto.pdf(x, scale = xm, b = a) for a in alp])      plt.plot(x, output.T)      plt.show()  paretoDist() Output:Exponential Distribution: It is a type of continuous distribution that determines the time elapsed between events (in a Poisson process). Let’s suppose, that you have the Poisson distribution model that holds the number of events happening in a given period. We can model the time between each birth using an exponential distribution.Here is a code example showing the use of Pareto Distribution – from numpy import random  import matplotlib.pyplot as mpl  import seaborn as sb  def expDist():      sb.distplot(random.exponential(size = 1200), hist = True)      mpl.show()   expDist()Output:Types of the Discrete probability distribution – There are various types of Discrete Probability Distribution a Data science aspirant should know about. Some of them are – Binomial Distribution: It is one of the popular discrete distributions that determine the probability of x success in the 'n' trial. We can use Binomial distribution in situations where we want to extract the probability of SUCCESS or FAILURE from an experiment or survey which went through multiple repetitions. A Binomial distribution holds a fixed number of trials. Also, a binomial event should be independent, and the probability of obtaining failure or success should remain the same. Here is a code example showing the use of Binomial Distribution – from numpy import random  import matplotlib.pyplot as mpl  import seaborn as sb    def binomialDist():      sb.distplot(random.normal(loc = 50, scale = 6, size = 1200), hist = False, label = 'normal')      sb.distplot(random.binomial(n = 100, p = 0.6, size = 1200), hist = False, label = 'binomial')      plt.show()    binomialDist() Output:Geometric Distribution: The geometric probability distribution is one of the crucial types of continuous distributions that determine the probability of any event having likelihood ‘p’ and will happen (occur) after 'n' number of Bernoulli trials. Here 'n' is a discrete random variable. In this distribution, the experiment goes on until we encounter either a success or a failure. The experiment does not depend on the number of trials. Here is a code example showing the use of Geometric Distribution – import matplotlib.pyplot as mpl  def probability_to_occur_at(attempt, probability):      return (1-p)**(attempt - 1) * probability  p = 0.3  attempt = 4  attempts_to_show = range(21)[1:]  print('Possibility that this event will occur on the 7th try: ', probability_to_occur_at(attempt, p))  mpl.xlabel('Number of Trials')  mpl.ylabel('Probability of the Event')  barlist = mpl.bar(attempts_to_show, height=[probability_to_occur_at(x, p) for x in attempts_to_show], tick_label=attempts_to_show)  barlist[attempt].set_color('g')  mpl.show() Output:Poisson Distribution: Poisson distribution is one of the popular types of discrete distribution that shows how many times an event has the possibility of occurrence in a specific set of time. We can obtain this by limiting the Bernoulli distribution from 0 to infinity. Data analysts often use the Poisson distributions to comprehend independent events occurring at a steady rate in a given time interval. Here is a code example showing the use of Poisson Distribution from scipy.stats import poisson  import seaborn as sb  import numpy as np  import matplotlib.pyplot as mpl  def poissonDist():       mpl.figure(figsize = (10, 10))      data_binom = poisson.rvs(mu = 3, size = 5000)      ax = sb.distplot(data_binom, kde=True, color = 'g',                       bins=np.arange(data_binom.min(), data_binom.max() + 1),                       kde_kws={'color': 'y', 'lw': 4, 'label': 'KDE'})      ax.set(xlabel = 'Poisson Distribution', ylabel='Data Frequency')      mpl.show()      poissonDist() Output:Multinomial Distribution: A multinomial distribution is another popular type of discrete probability distribution that calculates the outcome of an event having two or more variables. The term multi means more than one. The Binomial distribution is a particular type of multinomial distribution with two possible outcomes - true/false or heads/tails. Here is a code example showing the use of Multinomial Distribution – import numpy as np  import matplotlib.pyplot as mpl  np.random.seed(99)   n = 12                      pvalue = [0.3, 0.46, 0.22]     s = []  p = []     for size in np.logspace(2, 3):      outcomes = np.random.multinomial(n, pvalue, size=int(size))        prob = sum((outcomes[:,0] == 7) & (outcomes[:,1] == 2) & (outcomes[:,2] == 3))/len(outcomes)      p.append(prob)      s.append(int(size))  fig1 = mpl.figure()  mpl.plot(s, p, 'o-')  mpl.plot(s, [0.0248]*len(s), '--r')  mpl.grid()  mpl.xlim(xmin = 0)  mpl.xlabel('Number of Events')  mpl.ylabel('Function p(X = K)') Output:Negative Binomial Distribution: It is also a type of discrete probability distribution for random variables having negative binomial events. It is also known as the Pascal distribution, where the random variable tells us the number of repeated trials produced during a specific number of experiments.  Here is a code example showing the use of Negative Binomial Distribution – import matplotlib.pyplot as mpl   import numpy as np   from scipy.stats import nbinom    x = np.linspace(0, 6, 70)   gr, kr = 0.3, 0.7        g = nbinom.ppf(x, gr, kr)   s = nbinom.pmf(x, gr, kr)   mpl.plot(x, g, "*", x, s, "r--") Output: Apart from these mentioned distribution types, various other types of probability distributions exist that data science professionals can use to extract reliable datasets. In the next topic, we will understand some interconnections & relationships between various types of probability distributions. Relationship between various Probability distributions – It is surprising to see that different types of probability distributions are interconnected. In the chart shown below, the dashed line is for limited connections between two families of distribution, whereas the solid lines show the exact relationship between them in terms of transformation, variable, type, etc. Conclusion  Probability distributions are prevalent among data analysts and data science professionals because of their wide usage. Today, companies and enterprises hire data science professionals in many sectors, namely, computer science, health, insurance, engineering, and even social science, where probability distributions appear as fundamental tools for application. It is essential for Data analysts and data scientists. to know the core of statistics. Probability Distributions perform a requisite role in analyzing data and cooking a dataset to train the algorithms efficiently. If you want to learn more about data science - particularly probability distributions and their uses, check out KnowledgeHut's comprehensive Data science course. 
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Types of Probability Distributions Every Data Scie...

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Top Data Analytics Certifications

What is data analytics?In the world of IT, every small bit of data count; even information that looks like pure nonsense has its significance. So, how do we retrieve the significance from this data? This is where Data Science and analytics comes into the picture.  Data Analytics is a process where data is inspected, transformed and interpreted to discover some useful bits of information from all the noise and make decisions accordingly. It forms the entire basis of the social media industry and finds a lot of use in IT, finance, hospitality and even social sciences. The scope in data analytics is nearly endless since all facets of life deal with the storage, processing and interpretation of data.Why data analytics? Data Analytics in this Information Age has nearly endless opportunities since literally everything in this era hinges on the importance of proper processing and data analysis. The insights from any data are crucial for any business. The field of data Analytics has grown more than 50 times from the early 2000s to 2021. Companies specialising in banking, healthcare, fraud detection, e-commerce, telecommunication, infrastructure and risk management hire data analysts and professionals every year in huge numbers.Need for certification:Skills are the first and foremost criteria for a job, but these skills need to be validated and recognised by reputed organisations for them to impress a potential employer. In the field of Data Analytics, it is pretty crucial to show your certifications. Hence, an employer knows you have hands-on experience in the field and can handle the workload of a real-world setting beyond just theoretical knowledge. Once you get a base certification, you can work your way up to higher and higher positions and enjoy lucrative pay packages. Top Data Analytics Certifications Certified Analytics Professional (CAP) Microsoft Certified Azure Data Scientist Associate Cloudera Certified Associate (CCA) Data Analyst Associate Certified Analytics Professional (aCAP) SAS Certified Data Analyst (Using SAS91. Certified Analytics Professional (CAP)A certification from an organisation called INFORMS, CAP is a notoriously rigorous certification and stands out like a star on an applicant's resume. Those who complete this program gain an invaluable credential and are able to distinguish themselves from the competition. It gives a candidate a comprehensive understanding of the analytical process's various fine aspects--from framing hypotheses and analytic problems to the proper methodology, along with acquisition, model building and deployment process with long-term life cycle management. It needs to be renewed after three years.The application process is in itself quite complex, and it also involves signing the CAP Code of Ethics before one is given the certification. The CAP panel reviews each application, and those who pass this review are the only ones who can give the exam.  Prerequisite: A bachelor’s degree with 5 years of professional experience or a master's degree with 3 years of professional experience.  Exam Fee & Format: The base price is $695. For individuals who are members of INFORMS the price is $495. (Source) The pass percentage is 70%. The format is a four option MCQ paper. Salary: $76808 per year (Source) 2. Cloudera Certified Associate (CCA) Data Analyst Cloudera has a well-earned reputation in the IT sector, and its Associate Data analyst certification can help bolster the resume of Business intelligence specialists, system architects, data analysts, database administrators as well as developers. It has a specific focus on SQL developers who aim to show their proficiency on the platform.This certificate validates an applicant's ability to operate in a CDH environment by Cloudera using Impala and Hive tools. One doesn't need to turn to expensive tuitions and academies as Cloudera offers an Analyst Training course with almost the same objectives as the exam, leaving one with a good grasp of the fundamentals.   Prerequisites: basic knowledge of SQL and Linux Command line Exam Fee & Format: The cost of the exam is $295 (Source), The test is a performance-based test containing 8-12 questions to be completed in a proctored environment under 129 minutes.  Expected Salary: You can earn the job title of Cloudera Data Analyst that pays up to $113,286 per year. (Source)3. Associate Certified Analytics Professional (aCAP)aCAP is an entry-level certification for Analytics professionals with lesser experience but effective knowledge, which helps in real-life situations. It is for those candidates who have a master’s degree in a field related to data analytics.  It is one of the few vendor-neutral certifications on the list and must be converted to CAP within 6 years, so it offers a good opportunity for those with a long term path in a Data Analytics career. It also needs to be renewed every three years, like the CAP certification. Like its professional counterpart, aCAP helps a candidate step out in a vendor-neutral manner and drastically increases their professional credibility.  Prerequisite: Master’s degree in any discipline related to data Analytics. Exam Fee: The base price is $300. For individuals who are members of INFORMS the price is $200. (Source). There is an extensive syllabus which covers: i. Business Problem Framing, ii. Analytics Problem Framing, iii. Data, iv. Methodology Selection, v. Model Building, vi. Deployment, vii. Lifecycle Management of the Analytics process, problem-solving, data science and visualisation and much more.4. SAS Certified Data Analyst (Using SAS9)From one of the pioneers in IT and Statistics - the SAS Institute of Data Management - a SAS Certified Data Scientist can gain insights and analyse various aspects of data from businesses using tools like the SAS software and other open-source methodology. It also validates competency in using complex machine learning models and inferring results to interpret future business strategy and release models using the SAS environment. SAS Academy for Data Science is a viable institute for those who want to receive proper training for the exam and use this as a basis for their career.  Prerequisites: To earn this credential, one needs to pass 5 exams, two from the SAS Certified Big Data Professional credential and three exams from the SAS Certified Advanced Analytics Professional Credential. Exam Fee: The cost for each exam is $180. (Source) An exception is Predictive Modelling using the SAS Enterprise Miner, costing $250, This exam can be taken in the English language. One can join the SAS Academy for Data Science and also take a practice exam beforehand. Salary: You can get a job as a SAS Data Analyst that pays up to $90,000 per year! (Source) 5. IBM Data Science Professional CertificateWhenever someone studies the history of a computer, IBM (International Business Machines) is the first brand that comes up. IBM is still alive and kicking, now having forayed into and becoming a major player in the Big Data segment. The IBM Data Science Professional certificate is one of the beginner-level certificates if you want to sink your hands into the world of data analysis. It shows a candidate's skills in various topics pertaining to data sciences, including various open-source tools, Python databases, SWL, data visualisation, and data methodologies.  One needs to complete nine courses to earn the certificate. It takes around three months if one works twelve hours per week. It also involves the completion of various hands-on assignments and building a portfolio. A candidate earns the Professional certificate from Coursera and a badge from IBM that recognises a candidate's proficiency in the area. Prerequisites: It is the optimal course for freshers since it requires no requisite programming knowledge or proficiency in Analytics. Exam Fee: It costs $39 per month (Source) to access the course materials and the certificate. The course is handled by the Coursera organisation. Expected Salary: This certification can earn you the title of IBM Data Scientist and help you earn a salary of $134,846 per annum. (Source) 6. Microsoft Certified Azure Data Scientist AssociateIt's one of the most well-known certifications for newcomers to step into the field of Big Data and Data analytics. This credential is offered by the leader in the industry, Microsoft Azure. This credential validates a candidate's ability to work with Microsoft Azure developing environment and proficiency in analysing big data, preparing data for the modelling process, and then progressing to designing models. One advantage of this credential is that it has no expiry date and does not need renewal; it also authorises the candidate’s extensive knowledge in predictive Analytics. Prerequisites: knowledge and experience in data science and using Azure Machine Learning and Azure Databricks. Exam Fee: It costs $165 to (Source) register for the exam. One advantage is that there is no need to attend proxy institutions to prepare for this exam, as Microsoft offers free training materials as well as an instructor-led course that is paid. There is a comprehensive collection of resources available to a candidate. Expected Salary: The job title typically offered is Microsoft Data Scientist and it typically fetches a yearly pay of $130,993.(Source) Why be a Data Analytics professional? For those already working in the field of data, being a Data Analyst is one of the most viable options. The salary of a data analyst ranges from $65,000 to $85,000 depending on number of years of experience. This lucrative salary makes it worth the investment to get a certification and advance your skills to the next level so that you can work for multinational companies by interpreting and organising data and using this analysis to accelerate businesses. These certificates demonstrate that you have the required knowledge needed to operate data models of the volumes needed by big organizations. 1. Demand is more than supply With the advent of the Information Age, there has been a huge boom in companies that either entirely or partially deal with IT. For many companies IT forms the core of their business. Every business has to deal with data, and it is crucial to get accurate insights from this data and use it to further business interests and expand profits. The interpretation of data also aims to guide them in the future to make the best business decisions.  Complex business intelligence algorithms are in place these days. They need trained professionals to operate them; since this field is relatively new, there is a shortage of experts. Thus, there are vacancies for data analyst positions with lucrative pay if one is qualified enough.2. Good pay with benefitsA data analyst is an extremely lucrative profession, with an average base pay of $71,909 (Source), employee benefits, a good work-home balance, and other perks. It has been consistently rated as being among the hottest careers of the decade and allows professionals to have a long and satisfying career.   Companies Hiring Certified Data Analytics Professionals Oracle A California based brand, Oracle is a software company that is most famous for its data solutions. With over 130000 employees and a revenue of 39 billion, it is surely one of the bigger players in Data Analytics.  MicroStrategy   Unlike its name, this company is anything but micro, with more than 400 million worth of revenue. It provides a suite of analytical products along with business mobility solutions. It is a key player in the mobile space, working natively with Android and iOS.   SAS   One of the companies in the list which provides certifications and is also without a doubt one of the largest names in the field of Big Data, machine learning and Data Analytics, is SAS. The name SAS is derived from Statistical Analysis System. This company is trusted and has a solid reputation. It is also behind the SAS Institute for Data Science. Hence, SAS is the organisation you would want to go to if you're aiming for a long-term career in data science.    Conclusion To conclude, big data and data Analytics are a field of endless opportunities. By investing in the right credential, one can pave the way to a viable and lucrative career path. Beware though, there are lots of companies that provide certifications, but only recognised and reputed credentials will give you the opportunities you are seeking. Hiring companies look for these certifications as a mark of authenticity of your hands-on experience and the amount of work you can handle effectively. Therefore, the credential you choose for yourself plays a vital role in the career you can have in the field of Data analytics.  Happy learning!    
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Why Should You Start a Career in Machine Learning?

If you are even remotely interested in technology you would have heard of machine learning. In fact machine learning is now a buzzword and there are dozens of articles and research papers dedicated to it.  Machine learning is a technique which makes the machine learn from past experiences. Complex domain problems can be resolved quickly and efficiently using Machine Learning techniques.  We are living in an age where huge amounts of data are produced every second. This explosion of data has led to creation of machine learning models which can be used to analyse data and to benefit businesses.  This article tries to answer a few important concepts related to Machine Learning and informs you about the career path in this prestigious and important domain.What is Machine Learning?So, here’s your introduction to Machine Learning. This term was coined in the year 1997. “A computer program is said to learn from experience E with respect to some class of tasks T and performance measure P, if its performance at the tasks improves with the experiences.”, as defined in the book on ML written by Mitchell in 1997. The difference between a traditional programming and programming using Machine Learning is depicted here, the first Approach (a) is a traditional approach, and second approach (b) is a Machine Learning based approach.Machine Learning encompasses the techniques in AI which allow the system to learn automatically looking at the data available. While learning, the system tries to improve the experience without making any explicit efforts in programming. Any machine learning application follows the following steps broadlySelecting the training datasetAs the definition indicates, machine learning algorithms require past experience, that is data, for learning. So, selection of appropriate data is the key for any machine learning application.Preparing the dataset by preprocessing the dataOnce the decision about the data is made, it needs to be prepared for use. Machine learning algorithms are very susceptible to the small changes in data. To get the right insights, data must be preprocessed which includes data cleaning and data transformation.  Exploring the basic statistics and properties of dataTo understand what the data wishes to convey, the data engineer or Machine Learning engineer needs to understand the properties of data in detail. These details are understood by studying the statistical properties of data. Visualization is an important process to understand the data in detail.Selecting the appropriate algorithm to apply on the datasetOnce the data is ready and understood in detail, then appropriate Machine Learning algorithms or models are selected. The choice of algorithm depends on characteristics of data as well as type of task to be performed on the data. The choice also depends on what kind of output is required from the data.Checking the performance and fine-tuning the parameters of the algorithmThe model or algorithm chosen is fine-tuned to get improved performance. If multiple models are applied, then they are weighed against the performance. The final algorithm is again fine-tuned to get appropriate output and performance.Why Pursue a Career in Machine Learning in 2021?A recent survey has estimated that the jobs in AI and ML have grown by more than 300%. Even before the pandemic struck, Machine Learning skills were in high demand and the demand is expected to increase two-fold in the near future.A career in machine learning gives you the opportunity to make significant contributions in AI, the future of technology. All the big and small businesses are adopting Machine Learning models to improve their bottom-line margins and return on investment.  The use of Machine Learning has gone beyond just technology and it is now used in diverse industries including healthcare, automobile, manufacturing, government and more. This has greatly enhanced the value of Machine Learning experts who can earn an average salary of $112,000.  Huge numbers of jobs are expected to be created in the coming years.  Here are a few reasons why one should pursue a career in Machine Learning:The global machine learning market is expected to touch $20.83B in 2024, according to Forbes.  We are living in a digital age and this explosion of data has made the use of machine learning models a necessity. Machine Learning is the only way to extract meaning out of data and businesses need Machine Learning engineers to analyze huge data and gain insights from them to improve their businesses.If you like numbers, if you like research, if you like to read and test and if you have a passion to analyse, then machine learning is the career for you. Learning the right tools and programming languages will help you use machine learning to provide appropriate solutions to complex problems, overcome challenges and grow the business.Machine Learning is a great career option for those interested in computer science and mathematics. They can come up with new Machine Learning algorithms and techniques to cater to the needs of various business domains.As explained above, a career in machine learning is both rewarding and lucrative. There are huge number of opportunities available if you have the right expertise and knowledge. On an average, Machine Learning engineers get higher salaries, than other software developers.Years of experience in the Machine Learning domain, helps you break into data scientist roles, which is not just among the hottest careers of our generation but also a highly respected and lucrative career. Right skills in the right business domain helps you progress and make a mark for yourself in your organization. For example, if you have expertise in pharmaceutical industries and experience working in Machine learning, then you may land job roles as a data scientist consultant in big pharmaceutical companies.Statistics on Machine learning growth and the industries that use MLAccording to a research paper in AI Multiple (https://research.aimultiple.com/ml-stats/), the Machine Learning market will grow to 9 Billion USD by the end of 2022. There are various areas where Machine Learning models and solutions are getting deployed, and businesses see an overall increase of 44% investments in this area. North America is one of the leading regions in the adoption of Machine Learning followed by Asia.The Global Machine Learning market will grow by 42% which is evident from the following graph. Image sourceThere is a huge demand for Machine Learning modelling because of the large use of Cloud Based Applications and Services. The pandemic has changed the face of businesses, making them heavily dependent on Cloud and AI based services. Google, IBM, and Amazon are just some of the companies that have invested heavily in AI and Machine Learning based application development, to provide robust solutions for problems faced by small to large scale businesses. Machine Learning and Cloud based solutions are scalable and secure for all types of business.ML analyses and interprets data patterns, computing and developing algorithms for various business purposes.Advantages of Machine Learning courseNow that we have established the advantages of perusing a career in Machine Learning, let’s understand from where to start our machine learning journey. The best option would be to start with a Machine Learning course. There are various platforms which offer popular Machine Learning courses. One can always start with an online course which is both effective and safe in these COVID times.These courses start with an introduction to Machine Learning and then slowly help you to build your skills in the domain. Many courses even start with the basics of programming languages such as Python, which are important for building Machine Learning models. Courses from reputed institutions will hand hold you through the basics. Once the basics are clear, you may switch to an offline course and get the required certification.Online certifications have the same value as offline classes. They are a great way to clear your doubts and get personalized help to grow your knowledge. These courses can be completed along with your normal job or education, as most are self-paced and can be taken at a time of your convenience. There are plenty of online blogs and articles to aid you in completion of your certification.Machine Learning courses include many real time case studies which help you in understanding the basics and application aspects. Learning and applying are both important and are covered in good Machine Learning Courses. So, do your research and pick an online tutorial that is from a reputable institute.What Does the Career Path in Machine Learning Look Like?One can start their career in Machine Learning domain as a developer or application programmer. But the acquisition of the right skills and experience can lead you to various career paths. Following are some of the career options in Machine Learning (not an exhaustive list):Data ScientistA data scientist is a person with rich experience in a particular business field. A person who has a knowledge of domain, as well as machine learning modelling, is a data scientist. Data Scientists’ job is to study the data carefully and suggest accurate models to improve the business.AI and Machine Learning EngineerAn AI engineer is responsible for choosing the proper Machine Learning Algorithm based on natural language processing and neural network. They are responsible for applying it in AI applications like personalized advertising.  A Machine Learning Engineer is responsible for creating the appropriate models for improvement of the businessData EngineerA Data Engineer, as the name suggests, is responsible to collect data and make it ready for the application of Machine Learning models. Identification of the right data and making it ready for extraction of further insights is the main work of a data engineer.Business AnalystA person who studies the business and analyzes the data to get insights from it is a Business Analyst. He or she is responsible for extracting the insights from the data at hand.Business Intelligence (BI) DeveloperA BI developer uses Machine Learning and Data Analytics techniques to work on a large amount of data. Proper representation of data to suit business decisions, using the latest tools for creation of intuitive dashboards is the role of a BI developer.  Human Machine Interface learning engineerCreating tools using machine learning techniques to ease the human machine interaction or automate decisions, is the role of a Human Machine Interface learning engineer. This person helps in generating choices for users to ease their work.Natural Language Processing (NLP) engineer or developerAs the name suggests, this person develops various techniques to process Natural Language constructs. Building applications or systems using machine learning techniques to build Natural Language based applications is their main task. They create multilingual Chatbots for use in websites and other applications.Why are Machine Learning Roles so popular?As mentioned above, the market growth of AI and ML has increased tremendously over the past years. The Machine Learning Techniques are applied in every domain including marketing, sales, product recommendations, brand retention, creating advertising, understanding the sentiments of customer, security, banking and more. Machine learning algorithms are also used in emails to ease the users work. This says a lot, and proves that a career in Machine Learning is in high demand as all businesses are incorporating various machine learning techniques and are improving their business.One can harness this popularity by skilling up with Machine Learning skills. Machine Learning models are now being used by every company, irrespective of their size--small or big, to get insights on their data and use these insights to improve the business. As every company wishes to grow faster, they are deploying more machine learning engineers to get their work done on time. Also, the migration of businesses to Cloud services for better security and scalability, has increased their requirement for more Machine Learning algorithms and models to cater to their needs.Introducing the Machine learning techniques and solutions has brought huge returns for businesses.  Machine Learning solution providers like Google, IBM, Microsoft etc. are investing in human resources for development of Machine Learning models and algorithms. The tools developed by them are popularly used by businesses to get early returns. It has been observed that there is significant increase in patents in Machine Learning domains since the past few years, indicating the quantum of work happening in this domain.Machine Learning SkillsLet’s visit a few important skills one must acquire to work in the domain of Machine Learning.Programming languagesKnowledge of programming is very important for a career in Machine Learning. Languages like Python and R are popularly used to develop applications using Machine Learning models and algorithms. Python, being the simplest and most flexible language, is very popular for AI and Machine Learning applications. These languages provide rich support of libraries for implementation of Machine Learning Algorithms. A person who is good in programming can work very efficiently in this domain.Mathematics and StatisticsThe base for Machine Learning is mathematics and statistics. Statistics applied to data help in understanding it in micro detail. Many machine learning models are based on the probability theory and require knowledge of linear algebra, transformations etc. A good understanding of statistics and probability increases the early adoption to Machine Learning domain.Analytical toolsA plethora of analytical tools are available where machine learning models are already implemented and made available for use. Also, these tools are very good for visualization purposes. Tools like IBM Cognos, PowerBI, Tableue etc are important to pursue a career as a  Machine Learning engineer.Machine Learning Algorithms and librariesTo become a master in this domain, one must master the libraries which are provided with various programming languages. The basic understanding of how machine learning algorithms work and are implemented is crucial.Data Modelling for Machine Learning based systemsData lies at the core of any Machine Learning application. So, modelling the data to suit the application of Machine Learning algorithms is an important task. Data modelling experts are the heart of development teams that develop machine learning based systems. SQL based solutions like Oracle, SQL Server, and NoSQL solutions are important for modelling data required for Machine Learning applications. MongoDB, DynamoDB, Riak are some important NOSQL based solutions available to process unstructured data for Machine Learning applications.Other than these skills, there are two other skills that may prove to be beneficial for those planning on a career in the Machine Learning domain:Natural Language processing techniquesFor E-commerce sites, customer feedback is very important and crucial in determining the roadmap of future products. Many customers give reviews for the products that they have used or give suggestions for improvement. These feedbacks and opinions are analyzed to gain more insights about the customers buying habits as well as about the products. This is part of natural language processing using Machine Learning. The likes of Google, Facebook, Twitter are developing machine learning algorithms for Natural Language Processing and are constantly working on improving their solutions. Knowledge of basics of Natural Language Processing techniques and libraries is must in the domain of Machine Learning.Image ProcessingKnowledge of Image and Video processing is very crucial when a solution is required to be developed in the area of security, weather forecasting, crop prediction etc. Machine Learning based solutions are very effective in these domains. Tools like Matlab, Octave, OpenCV are some important tools available to develop Machine Learning based solutions which require image or video processing.ConclusionMachine Learning is a technique to automate the tasks based on past experiences. This is among the most lucrative career choices right now and will continue to remain so in the future. Job opportunities are increasing day by day in this domain. Acquiring the right skills by opting for a proper Machine Learning course is important to grow in this domain. You can have an impressive career trajectory as a machine learning expert, provided you have the right skills and expertise.
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Why Should You Start a Career in Machine Learning?

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