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How to Interpret R Squared and Goodness of Fit in Regression Analysis

Regression Analysis is a set of statistical processes that are at the core of data science. In the field of numerical simulation, it represents the most well-understood models and helps in interpreting machine learning algorithms. Their real-life applications can be seen in a wide range of domains, ranging from advertising and medical research to agricultural science and even different sports. In linear regression models, R-squared is a goodness-fit-measure. It takes into account the strength of the relationship between the model and the dependent variable. Its convenience is measured on a scale of 0 – 100%. Once you have a fit linear regression model, there are a few considerations that you need to address: How well does the model fit the data? How well does it explain the changes in the dependent variable? In this article, we will learn about R-squared (R2), its interpretation, limitations, and a few miscellaneous insights about it. Let us first understand the fundamentals of Regression Analysis and its necessity. What is Regression Analysis? Regression Analysis is a well-known statistical learning technique that allows you to examine the relationship between the independent variables (or explanatory variables) and the dependent variables (or response variables). It requires you to formulate a mathematical model that can be used to determine an estimated value which is nearly close to the actual value. The two terms essential to understanding Regression Analysis: Dependent variables - The factors that you want to understand or predict. Independent variables - The factors that influence the dependent variable. Consider a situation where you are given data about a group of students on certain factors: number of hours of study per day, attendance, and scores in a particular exam. The Regression technique allows you to identify the most essential factors, the factors that can be ignored and the dependence of one factor on others.  There are mainly two objectives of a Regression Analysis technique: Explanatory analysis - This analysis understands and identifies the influence of the explanatory variable on the response variable concerning a certain model. Predictive analysis - This analysis is used to predict the value assumed by the dependent variable.  Why use Regression Analysis? The technique generates a regression equation where the relationship between the explanatory variable and the response variable is represented by the parameters of the technique. You can use the Regression Analysis to perform the following: To model different independent variables. To add continuous and categorical variables having numerous distinct groups based on a characteristic. To model the curvature using polynomial terms. To determine the effect of a certain independent variable on another variable by assessing the interaction terms.  What are Residuals? Residuals identify the deviation of observed values from the expected values. They are also referred to as error or noise terms. A residual gives an insight into how good our model is against the actual value but there are no real-life representations of residual values. Source:  hatarilabs.comRegression Line and residual plotsThe calculation of the real values of intercept, slope, and residual terms can be a complicated task. However, the Ordinary Least Square (OLS) regression technique can help us to speculate on an efficient model.  The technique minimizes the sum of the squared residuals. With the help of the residual plots, you can check whether the observed error is consistent with the stochastic error (differences between the expected and observed values must be random and unpredictable).  What is Goodness-of-Fit?  The Regression Analysis is a part of the linear regression technique. It examines an equation that reduces the distance between the fitted line and all of the data points. Determining how well the model fits the data is crucial in a linear model. A general idea is that if the deviations between the observed values and the predicted values of the linear model are small and unbiased, the model has a well-fit data.  In technical terms, “Goodness-of-fit” is a mathematical model that describes the differences between the observed values and the expected values or how well the model fits a set of observations. This measure can be used in statistical hypothesis testing. How to assess Goodness-of-fit in a regression model? According to statisticians, if the differences between the observations and the predicted values tend to be small and unbiased, we can say that the model fits the data well. The meaning of unbiasedness in this context is that the fitted values do not reach the extremes, i.e. too high or too low during observations. As we have seen earlier, a linear regression model gives you the outlook of the equation which represents the minimal difference between the observed values and the predicted values. In simpler terms, we can say that linear regression identifies the smallest sum of squared residuals probable for the dataset. Determining the residual plots represents a crucial part of a regression model and it should be performed before evaluating the numerical measures of goodness-of-fit, like R-squared. They help to recognize a biased model by identifying problematic patterns in the residual plots.  However, if you have a biased model, you cannot depend on the results. If the residual plots look good, you can assess the value of R-squared and other numerical outputs. What is R-squared? In data science, R-squared (R2) is referred to as the coefficient of determination or the coefficient of multiple determination in case of multiple regression.  In the linear regression model, R-squared acts as an evaluation metric to evaluate the scatter of the data points around the fitted regression line. It recognizes the percentage of variation of the dependent variable.  R-squared and the Goodness-of-fit R-squared is the proportion of variance in the dependent variable that can be explained by the independent variable.The value of R-squared stays between 0 and 100%: 0% corresponds to a model that does not explain the variability of the response data around its mean. The mean of the dependent variable helps to predict the dependent variable and also the regression model. On the other hand, 100% corresponds to a model that explains the variability of the response variable around its mean. If your value of R2  is large, you have a better chance of your regression model fitting the observations. Although you can get essential insights about the regression model in this statistical measure, you should not depend on it for the complete assessment of the model. It does not give information about the relationship between the dependent and the independent variables.  It also does not inform about the quality of the regression model. Hence, as a user, you should always analyze R2   along with other variables and then derive conclusions about the regression model. Visual Representation of R-squared You can have a visual demonstration of the plots of fitted values by observed values in a graphical manner. It illustrates how R-squared values represent the scatter around the regression line. As observed in the pictures above, the value of R-squared for the regression model on the left side is 17%, and for the model on the right is 83%. In a regression model, when the variance accounts to be high, the data points tend to fall closer to the fitted regression line.  However, a regression model with an R2 of 100% is an ideal scenario which is actually not possible. In such a case, the predicted values equal the observed values and it causes all the data points to fall exactly on the regression line.  Interpretation of R-squared The simplest interpretation of R-squared is how well the regression model fits the observed data values. Let us take an example to understand this. Consider a model where the  R2  value is 70%. This would mean that the model explains 70% of the fitted data in the regression model. Usually, when the R2  value is high, it suggests a better fit for the model.  The correctness of the statistical measure does not only depend on R2  but can depend on other several factors like the nature of the variables, the units on which the variables are measured, etc. So, a high R-squared value is not always likely for the regression model and can indicate problems too. A low R-squared value is a negative indicator for a model in general. However, if we consider the other factors, a low R2 value can also end up in a good predictive model. Calculation of R-squared R- squared can be evaluated using the following formula: Where: SSregression – Explained sum of squares due to the regression model. SStotal – The total sum of squares. The sum of squares due to regression assesses how well the model represents the fitted data and the total sum of squares measures the variability in the data used in the regression model. Now let us come back to the earlier situation where we have two factors: number of hours of study per day and the score in a particular exam to understand the calculation of R-squared more effectively. Here, the target variable is represented by the score and the independent variable by the number of hours of study per day.  In this case, we will need a simple linear regression model and the equation of the model will be as follows:  ŷ = w1x1 + bThe parameters w1  and  b can be calculated by reducing the squared error over all the data points. The following equation is called the least square function:minimize ∑(yi –  w1x1i – b)2Now, to calculate the goodness-of-fit, we need to calculate the variance:var(u) = 1/n∑(ui – ū)2where, n represents the number of data points. Now, R-squared calculates the amount of variance of the target variable explained by the model, i.e. function of the independent variable. However, in order to achieve that, we need to calculate two things: Variance of the target variable: var(avg) = ∑(yi – Ӯ)2Variance of the target variable around the best-fit line:var(model) = ∑(yi – ŷ)2Finally, we can calculate the equation of R-squared as follows:R2 = 1 – [var(model)/var(avg)] = 1 -[∑(yi – ŷ)2/∑(yi – Ӯ)2] Limitations of R-squared Some of the limitations of R-squared are: R-squared cannot be used to check if the coefficient estimates and predictions are biased or not. R-squared does not inform if the regression model has an adequate fit or not. To determine the biasedness of the model, you need to assess the residuals plots. A good model can have a low R-squared value whereas you can have a high R-squared value for a model that does not have proper goodness-of-fit.  Low R-squared and High R-squared values Regression models with low R2 do not always pose a problem. There are some areas where you are bound to have low R2 values. One such case is when you study human behavior. They tend to have R2  values less than 50%. The reason behind this is that predicting people is a more difficult task than predicting a physical process. You can draw essential conclusions about your model having a low R2 value when the independent variables of the model have some statistical significance. They represent the mean change in the dependent variable when the independent variable shifts by one unit. However, if you are working on a model to generate precise predictions, low R-squared values can cause problems. Now, let us look at the other side of the coin. A regression model with high R2  value can lead to – as the statisticians call it – specification bias. This type of situation arises when the linear model is underspecified due to missing important independent variables, polynomial terms, and interaction terms.  To overcome this situation, you can produce random residuals by adding the appropriate terms or by fitting a non-linear model. Model overfitting and data mining techniques can also inflate the value of R2. The model they generate might provide an excellent fit to the data but actually the results tend to be completely deceptive. ConclusionLet us summarize what we have covered in this article so far: Regression Analysis and its importance Residuals and Goodness-of-fit R-squared: Representation, Interpretation, Calculation, Limitations Low and High R2 values Although R-squared is a very intuitive measure to determine how well a regression model fits a dataset, it does not narrate the complete story. If you want to get the full picture, you need to have an in-depth knowledge of R2  along with other statistical measures and residual plots. For gaining more information on the limitations of the R-squared, you can learn about Adjusted R-squared and Predicted R-squared which provide different insights to assess a model’s goodness-of-fit. You can also take a look at a different type of goodness-of-fit measure, i.e. Standard Error of the Regression. 

How to Interpret R Squared and Goodness of Fit in Regression Analysis

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How to Interpret R Squared and Goodness of Fit in Regression Analysis

Regression Analysis is a set of statistical processes that are at the core of data science. In the field of numerical simulation, it represents the most well-understood models and helps in interpreting machine learning algorithms. Their real-life applications can be seen in a wide range of domains, ranging from advertising and medical research to agricultural science and even different sports. 

In linear regression models, R-squared is a goodness-fit-measure. It takes into account the strength of the relationship between the model and the dependent variable. Its convenience is measured on a scale of 0 – 100%. 

Once you have a fit linear regression model, there are few considerations that you need to address: 

  • How well does the model fit the data? 
  • How well does it explain the changes in the dependent variable? 

In this article, we will learn about R-squared (R2), its interpretation, limitations, and few miscellaneous insights about it. 

Let us first understand the fundamentals of Regression Analysis and its necessity. 

What is Regression Analysis? 

Regression Analysis is a well-known statistical learning technique that allows you to examine the relationship between the independent variables (or explanatory variables) and the dependent variables (or response variables). It requires you to formulate a mathematical model that can be used to determine an estimated value which is nearly close to the actual value. 

The two terms essential to understanding Regression Analysis: 

  • Dependent variables - The factors that you want to understand or predict. 
  • Independent variables - The factors that influence the dependent variable. 

Consider a situation where you are given data about a group of students on certain factors: number of hours of study per day, attendance, and scores in a particular exam. The Regression technique allows you to identify the most essential factors, the factors that can be ignored and the dependence of one factor on others.  

There are mainly two objectives of a Regression Analysis technique: 

  • Explanatory analysis - This analysis understands and identifies the influence of the explanatory variable on the response variable concerning a certain model. 
  • Predictive analysis - This analysis is used to predict the value assumed by the dependent variable.  

Why use Regression Analysis? 

The technique generates a regression equation where the relationship between the explanatory variable and the response variable is represented by the parameters of the technique. 

You can use the Regression Analysis to perform the following: 

  • To model different independent variables. 
  • To add continuous and categorical variables having numerous distinct groups based on a characteristic. 
  • To model the curvature using polynomial terms. 
  • To determine the effect of a certain independent variable on another variable by assessing the interaction terms.  

What are Residuals? 

Residuals identify the deviation of observed values from the expected values. They are also referred to as error or noise terms. A residual gives an insight into how good our model is against the actual value but there are no real-life representations of residual values. 

How To Interpret R squared and Goodness of Fit in Regression Analysis  

Source:  hatarilabs.com

Regression Line and residual plots

The calculation of the real values of intercept, slope, and residual terms can be a complicated task. However, the Ordinary Least Square (OLS) regression technique can help us to speculate on an efficient model.  The technique minimizes the sum of the squared residuals. With the help of the residual plots, you can check whether the observed error is consistent with the stochastic error (differences between the expected and observed values must be random and unpredictable).  

What is Goodness-of-Fit?  

The Regression Analysis is a part of the linear regression technique. It examines an equation that reduces the distance between the fitted line and all of the data points. Determining how well the model fits the data is crucial in a linear model. 

A general idea is that if the deviations between the observed values and the predicted values of the linear model are small and unbiased, the model has a well-fit data.  

In technical terms, “Goodness-of-fit” is a mathematical model that describes the differences between the observed values and the expected values or how well the model fits a set of observations. This measure can be used in statistical hypothesis testing. 

How to assess Goodness-of-fit in a regression model? 

According to statisticians, if the differences between the observations and the predicted values tend to be small and unbiased, we can say that the model fits the data well. The meaning of unbiasedness in this context is that the fitted values do not reach the extremes, i.e. too high or too low during observations. 

As we have seen earlier, a linear regression model gives you the outlook of the equation which represents the minimal difference between the observed values and the predicted values. In simpler terms, we can say that linear regression identifies the smallest sum of squared residuals probable for the dataset. 

Determining the residual plots represents a crucial part of a regression model and it should be performed before evaluating the numerical measures of goodness-of-fit, like R-squared. They help to recognize a biased model by identifying problematic patterns in the residual plots.  

However, if you have a biased model, you cannot depend on the results. If the residual plots look good, you can assess the value of R-squared and other numerical outputs. 

What is R-squared? 

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

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

R-squared and the Goodness-of-fit 

R-squared is the proportion of variance in the dependent variable that can be explained by the independent variable.

How To Interpret R squared and Goodness of Fit in Regression Analysis  

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

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

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

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

It also does not inform about the quality of the regression model. Hence, as a user, you should always analyze R2   along with other variables and then derive conclusions about the regression model. 

Visual Representation of R-squared 

You can have a visual demonstration of the plots of fitted values by observed values in a graphical manner. It illustrates how R-squared values represent the scatter around the regression line. How To Interpret R squared and Goodness of Fit in Regression Analysis  

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

However, a regression model with an R2 of 100% is an ideal scenario which is actually not possible. In such a case, the predicted values equal the observed values and it causes all the data points to fall exactly on the regression line.  

Interpretation of R-squared 

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

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

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

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

Calculation of R-squared 

R- squared can be evaluated using the following formula: How To Interpret R squared and Goodness of Fit in Regression Analysis  

Where: 

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

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

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

How To Interpret R squared and Goodness of Fit in Regression Analysis  In this case, we will need a simple linear regression model and the equation of the model will be as follows:  

ŷ = w1x1 + b

The parameters w1  and  b can be calculated by reducing the squared error over all the data points. The following equation is called the least square function:

minimize ∑(yi –  w1x1i – b)2

How To Interpret R squared and Goodness of Fit in Regression Analysis  

Now, to calculate the goodness-of-fit, we need to calculate the variance:

var(u) = 1/n∑(ui – ū)2

where, n represents the number of data points. 

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

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

  • Variance of the target variable: 

var(avg) = ∑(yi – Ӯ)2

  • Variance of the target variable around the best-fit line:

var(model) = ∑(yi – ŷ)2

How To Interpret R squared and Goodness of Fit in Regression Analysis  

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

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

Limitations of R-squared 

Some of the limitations of R-squared are: 

  • R-squared cannot be used to check if the coefficient estimates and predictions are biased or not. 
  • R-squared does not inform if the regression model has an adequate fit or not. 

To determine the biasedness of the model, you need to assess the residuals plots. A good model can have a low R-squared value whereas you can have a high R-squared value for a model that does not have proper goodness-of-fit.  

Low R-squared and High R-squared values 

Regression models with low R2 do not always pose a problem. There are some areas where you are bound to have low Rvalues. One such case is when you study human behavior. They tend to have R values less than 50%. The reason behind this is that predicting people is a more difficult task than predicting a physical process. 

You can draw essential conclusions about your model having a low Rvalue when the independent variables of the model have some statistical significance. They represent the mean change in the dependent variable when the independent variable shifts by one unit. 

However, if you are working on a model to generate precise predictions, low R-squared values can cause problems. 

Now, let us look at the other side of the coin. A regression model with high R2  value can lead to – as the statisticians call it – specification bias. This type of situation arises when the linear model is underspecified due to missing important independent variables, polynomial terms, and interaction terms.  

To overcome this situation, you can produce random residuals by adding the appropriate terms or by fitting a non-linear model. 

Model overfitting and data mining techniques can also inflate the value of R2. The model they generate might provide an excellent fit to the data but actually the results tend to be completely deceptive. 

Conclusion

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

  • Regression Analysis and its importance 
  • Residuals and Goodness-of-fit 
  • R-squared: Representation, Interpretation, Calculation, Limitations 
  • Low and High Rvalues 

Although R-squared is a very intuitive measure to determine how well a regression model fits a dataset, it does not narrate the complete story. If you want to get the full picture, you need to have an in-depth knowledge of R2  along with other statistical measures and residual plots. 

For gaining more information on the limitations of the R-squared, you can learn about Adjusted R-squared and Predicted R-squared which provide different insights to assess a model’s goodness-of-fit. You can also take a look at a different type of goodness-of-fit measure, i.e. Standard Error of the Regression. 

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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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Top Data Analytics Certifications

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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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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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