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Regression Analysis

What Is Regression Analysis?

Regression analysis is used to understand the relationship between two or more variables of interest. Often, this type of analysis examines the influences of one or more independent variables on a dependent variable. Furthermore, a regression analysis allows for a better understanding of the specific ways a dependent variable is affected by any one independent variable. In short, it answers how the dependent variable changes when varying one of the independent variables, while other independent variables remain unchanged?

How Does Regression Analysis Work?

The general function of regression analysis is the regression function, and it begins with covariance. The covariance shows the direction of the relationship, either positive or negative. If the relationship is positive, one variable would increase as another variable does. If the relationship is negative, as one variable increases, the other decreases. Next, the correlation coefficient is calculated by dividing the covariance by the product of the standard deviation of the two variables. This limits the correlation to a value range of -1 to 1. Lastly, a regression equation (y = bx + a) can be used to forecast at any variable, where "y" is the dependent variable, "b" is the slope of the line, "x" is the independent variable, and "a" represents the slope of the line. This form of linear regression is also known as ordinary least squares

Regression Analysis Visualized

The graph below visualizes a linear regression function across a specified data set. The red line represents the linear regression function and expresses the rate of change among the data points. 

A Linear Regression

Regression Analysis and Machine Learning

Because regression analysis is frequently used for forecasting and making predictions, it is widely integrated within the realm of machine learning, specifically supervised learning. A regression analysis can be used to understand how independent variables are related to the dependent variable, and examine the relationship between the two. In some circumstances, a regression analysis can be used to infer a causal relationship between two variables, however it is often advised to use regression analysis in conjunction with other tests to avoid false relationships. 

With the use of regression analysis, machine learning is able to make better predictions about any given outcome due to the patterns of interactions between variables as exemplified by regression functions.