Multiple Linear Regression

Abstract

Multiple linear regression represents a generalization to more than a single explanatory variable of the simple linear regression model introduced in Chapter 4. The aim of this type of regression is to model the relationship between a random response variable and a number of explanatory variables. Strictly speaking, the values of the explanatory variable are assumed to be known, or under the control of the investigator; in other words, they are not considered to be random variables. In most applications of multiple regression, however, the observed values of the explanatory variables will, like the response variable, be subject to random variation. Parameter estimation and inference is then considered conditional on the observed values of the explanatory variables.