Authors: Scott H. Brown

Summary

     Simple linear regression is a fundamental technique in statistics to demonstrate a relationship between dependent and independent variables. Multiple linear regression is an extension of simple linear regression. It is used to find the relationship of several independent variables to a single dependent variable unlike simple linear regression where independent variable is also only one like dependent variable. A simple linear regression is of the form

The extended form for multiple linear regression is of the form

Such a system can be written in matrix notation like this

In this equation, β needs to be determined and  is an error term. If the system is solved for  which is our required goal, the system takes a form of

from where

To calculate the error term, we need to find the difference in the values of the dependent variable for the given data and the equation. Squaring and summing these terms will give sum of squares of residuals which tells the goodness of fit.

This paper is an insight into the mathematics of multiple linear regression and is helpful in writing its code in MATLAB for future use.

Other multivariate techniques like, cluster analysis, principal component analysis (PCA), and factor analysis are an extension of this model and can be understood on the basis of multiple linear regression. An insight into mathematics makes research more powerful to support the results.

Reviewer: Aamir Alaud-din

aamiralauddin@gist.ac.kr