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Linear Regression in Data Science - A Complete Overview

 

Data science is all about analyzing large sets of data to identify trends or patterns. Additionally, data science powers business decisions by allowing accurate predictions.

 

There are several ways and models to leverage data science to make forecasts. Among them, linear regression is a popular technique used by data scientists around the world. The method allows you to predict the value of one factor based on other factors. Therefore, linear regressions deal with two or more variables.

 

The variable data scientists want to predict is referred to as a dependent variable. Consequently, the variable scientists rely on to make the prediction is named the independent variable.

 

Linear regression is among the simple methods to predict accurately in data science. Additionally, the mathematical formula is easy to comprehend and work with. Best of all, you can use linear regression to make forecasts for several domains. For example, businesses may use linear regressions to see how price changes affect the demand for a product.

 

Additionally, linear regressions have ample use in the educational sector. It can go a long way to determine the effectiveness of courses and evaluate student performance.

 

Moreover, linear regression may be applicable to the sports industry. Clubs may use the technique to find out if there is any relationship between games won and points scored per game.

 

In addition, linear regression may allow them to establish the relationship between different variables. Clubs may find out the relationship between wins, points scored by teams, and even points scored by rivals.

 

However, this is not the end of the use of linear regressions. They are also common to spheres such as biology, psychology, environmental science, and more. The method provides a scientific way to predict future outcomes accurately.

 

In this blog, we will explore linear regression in depth. Additionally, we will cover essential topics like simple linear regression and coefficient of determination.

 

Statistical Learning Theory

 

Linear regression comes from the field of statistics. Therefore, data scientists use many statistical methods to make assumptions through linear regressions.

 

As noted earlier, linear regression is an excellent way to make predictions and establish the relationship between multiple variables.

 

However, you need a statistical model to provide a structure and work with your data. In such cases, the statistical learning theory may be helpful. It is a high-level framework that is best for reviewing the statistical interference issue of making predictions based on data.

 

In the realm of data science, statistical learning theory is strictly applied to machine learning. However, the method still works on the principles of functional analysis and statistics.

 

What is the use of statistical learning theory in data science?

 

The goal of statistical learning theory is pretty simple in the case of data science. It allows data scientists to generate a model that is able to make inferences from data fed to it.

 

In addition, the model makes way for reliable predictions.

 

Statistical learning theory works with dependent and independent variables of linear regression. The independent variable stays unchanged even if the other variables keep on changing.

 

In addition, the independent variable impacts the behavior of the dependent variable.

 

For example, the age of a person is an independent variable. It cannot change no matter what anyone does or says.

 

Consequently, dependent variables can change and don’t remain the same. Examples of dependent variables may be the age or height of a person. They are affected by the independent variable or the age of the person.

 

If you are using a graph, you will plot your independent variable along the ‘X-axis. Additionally, you have to plot the dependent variable along the ‘Y-axis.

 

Statistical learning theory is a great tool in the hands of data scientists. It has contributed heavily to fields such as speech recognition, digital vision, and bioinformatics.

 

Simple Linear Regression

Simple linear regression is an ideal method to establish the relationship between two quantifiable variables. By quantifiable, we mean the variables can be expressed in numbers.

 

Additionally, one is an independent variable, while the other is the dependent variable.

 

Simple linear regression is suitable to determine the statistical relationship between two variables. However, it cannot be used to establish a deterministic relationship between variables.

 

A deterministic relationship is one where you can express one variable in terms of the other. For example, you may use kilometers to predict the speed in miles per hour accurately.

 

Instead, simple linear regression is suitable to derive a line that aligns with the data perfectly. Additionally, the line should have a minimal total prediction error to provide accurate results.

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Data scientists rely on simple linear regression for various purposes. They may use the technique to study how viable the relationship is between the predictors.

 

For example, they may find out how rainfall affects soil erosion through simple linear regression.

 

Or, they may use the technique to determine how one variable changes when the other one changes.

 

For example, the method may help them find out the amount of soil erosion caused by different levels of rainfall.

 

Simple linear regression is also apt for machine learning. Computers can learn from training sets of data to provide accurate predictions.

 

Let’s say you have a set of data that informs the hours studied by every student and the grades they achieved.

 

Now, you want to find out how the grades change when you vary the hours studied.

 

So, you will first feed training data to your system. In this case, it is the hours studied and grades obtained by the students.

 

Next, you can obtain a regression line that contains the most negligible errors. Now, you can use this regression line to make predictions with new data.

 

So, you can now vary the hours studied by the students and see what grades they might get.

 

Coefficient of Determination

 

Statistical learning theory and simple linear regression are two methods used by data scientists. However, there are other ways in linear regression that help scientists deal with complex predictions.

 

As discussed earlier, these methods may allow you to establish a relationship or correlations between variables. However, correlations may not always give you the full picture, especially for tasks like identifying trends.

 

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In such cases, you need to know how one correlation matches with the other. So, you will need to use a coefficient of determination to fulfill your goal. It allows data scientists to find out how well the predicted values align with the observed variables.

 

Or in other words, it assesses how a difference in one variable might be reasoned by the changes of the other variable for a given outcome.

 

The coefficient of determination is also known by other names such as r2 or r-squared. However, you don’t have to find out the square of anything.

 

Instead of the best fitting line, the coefficient of determination uses the 1:1 line. Additionally, it focuses on the distance between the values to make accurate predictions.

 

The aim is to work with data closest to the 1:1 line as the coefficient of determination is higher.

 

Data scientists denote the coefficient of determination as r2. You may have three types of predictions based on the data:

 

●      r2 is equal to 0 - it tells the predictions are no better than guesses based on the observed values

 

●      r2 is equal to +1 - shows the predictions align with the observed values efficiently

 

●      r2 is negative - indicates the predictions are inferior to random guesses

                                                                     

The coefficient of determination is an ideal tool to validate correlations established by other statistical models of linear regression. Additionally, it can be used to predict future outcomes or validate hypotheses based on available data.

 

 Assumptions for Linear Regression

 

Data scientists work with four major assumptions when using linear regression. They are described below:

 

Independence of Observations

 

There cannot be any relationship between different examples when working with linear regression. However, it is not easy to determine independence by just going through your data.

 

Rather, you have to try to find out the relationship during data collection. For example, clinical trials that choose and group participants randomly can establish the independence of observance successfully.

 

No Variables Are Missing or Hidden

 

The statistical model you use for linear regression should contain all the applicable explanatory variables. Otherwise, your model will become inaccurate and deliver the wrong predictions.

 

In addition, the model will attempt to dedicate coefficients to variables that are present in your data. As a result, it will give rise to what is known as the misspecification of statistical models.

 

You should first try to add a variable to your model and assess the impact. If the model appears inaccurate or changes too much due to the variable, it is an important one.

 

In that case, you will have to start from scratch and fall back on your data collection to identify relevant data.

 

A Linear Relationship

 

Linear regression is meant for investigating linear relations between variables. Therefore, the independent and dependent predictors you are working with must have a linear relation.

 

This goes without saying, but you may not find it mentioned everywhere. You are to use a linear model for analyzing linear relations only.

 

If the relation is non-linear, then you should choose from one of the non-linear models available.

 

It is possible to determine the relationship between your independent and dependent variables with scatter plots.

 

Minimal Multicollinearity

 

Data scientists are happy when there are strong correlations between an independent and dependent predictor.

 

However, they don’t want any strong correlation between the independent variables. The reason is that independent variables determine or influence the behavior of the dependent variable.

 

Therefore, if independent variables are correlated strongly, they end up explaining the same phenomenon.

 

As a result, data scientists will be unable to determine which independent variable is responsible for the behavior.

 

Regression Diagnostics in Stats Model

 

The stats model data scientists use to analyze relations between variables should be reliable. It should be able to fulfill all the assumptions of linear regression and align with the recorded data.

 

Data scientists can use regression diagnostics to check the reliability of their stats model. The diagnostics rely on numerical and graphical tools to assess if the assumptions of the model are met.

 

Additionally, the tests determine if the model and data are consistent with the data in the books.

 

Regression diagnostics try to identify the extreme points or outliers that might influence the regression. Data scientists also look for outliers that may be manipulating the results of the analysis.

Moreover, regression diagnostic evaluates if any strong correlation between the independent predictors is influencing the outcomes.

 

There are various ways to perform regression diagnostics. One of the most popular methods is plotting the residuals. Plots are ideal for determining if the errors are regularly distributed.

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In addition, it also tries to find out if there are any patterns among the residuals.

 

Data scientists may also use other methods for performing diagnostics on stats models. For example, they may try to identify the presence of data points that affect the estimation of coefficients majorly.

 

Final Thoughts

 

Linear regression is a suitable tool for data scientists to work with one or more variables. It can be used to determine relationships between variables and analyze the correlation between predictors. Simple linear regression is also a good way to evaluate the relations between two variables. Data scientists may use different statistical models to perform linear regression and predict future outcomes efficiently. They may also test hypotheses with linear regression.