Principles of Managerial Statistics and Data Science

14Multiple Linear Regression

14.1 Introduction

Simple linear regression is used when our aim is to determine the association between a response variable and only one predictor. Of course, there are situations when we observe several predictors along with the response variable.

What If Important Predictors Are Not Accounted For?

Leaving important predictors out of the model leads to a biased slope estimate in the simple linear model. Also, by including important predictors, better estimates of are obtained from the model.

In some instances, all predictors are of interest. In other instances, only some are of real interest, but we must account for other variables. Multiple linear regression is the extremely useful procedure performed when more than one predictor is used in the linear model. It may seem that this is a trivial extension to simple linear regression, but there are complications that arise. Although statistical software will perform multiple linear regression with a click of a button, there are many ways to conduct this type of analysis and one must know how to select the apt methods. We will cover the fundamental aspects of multiple linear regression, but because of these complications, we highly recommend that this type of analysis be done by a professional statistician.

Goal of the Analysis

Generally, regression methods have two main objectives:

• explaining ...