Regression Analysis

What is Regression Analysis?

Regression analysis is a statistical method used to model and analyze the relationship between a dependent variable and one or more independent variables. It aims to understand how changes in the independent variables are associated with changes in the dependent variable.

In regression analysis, the dependent variable is the variable of interest that we want to predict or explain, while the independent variables are the variables used to predict or explain the dependent variable.

There are several types of regression analysis, but the most common one is linear regression which is known as ordinary least squares (OLS) regression. In linear regression, the relationship between the dependent variable and independent variables is assumed to be linear. The goal is to find the best-fitting line (or hyperplane in higher dimensions) that minimizes the difference between the predicted values and the actual values of the dependent variable.

            The linear regression equation can be written as:

             Y = β0 + β1X1 + β2X2 + ... + βnXn + ε

                    Where:

• Y is the dependent variable.
• X1, X2, ..., Xn are the independent variables.
• β0 is the intercept
• β1, β2, ..., βn are the coefficients that represent the effect of each independent variable on the dependent variable.
• ε is the error term, representing the discrepancy between the predicted and actual values.

• Note: If you have not seen the equation above before, you may be more familar with the equation:

                Y = MX + B

                    

                    Where:

                        Y is the dependent variable.

                        X is the independent variable

                        M is the slope of the relationship between x and y

                        B is the intercept

• The linear regression equation is fundamentally the same as the y=mx + b equation
• β0 and B are the same, representing intercepts
• β1, β2 and M are the same, representing slope coefficients

The coefficients (β values) obtained from the regression analysis provide information about the direction and magnitude of the relationship between the independent variables and the dependent variable. A positive coefficient indicates a positive relationship, while a negative coefficient indicates a negative relationship. The magnitude of the coefficient indicates the strength of the relationship.

Regression analysis allows for various applications, including prediction, forecasting, and understanding the influence of different factors on a particular outcome. It is widely used in fields such as economics, social sciences, finance, marketing, and many others to gain insights and make informed decisions based on the relationship between variables.