Probability and Statistics for Engineers and Scientists, Updated 9th Edition, by Pearson

Chapter 12

Multiple Linear Regression and Certain Nonlinear Regression Models

12.1 Introduction

In most research problems where regression analysis is applied, more than one independent variable is needed in the regression model. The complexity of most scientific mechanisms is such that in order to be able to predict an important response, a multiple regression model is needed. When this model is linear in the coefficients, it is called a multiple linear regression model. For the case of k independent variables x₁, x₂, …, x_k, the mean of Y|x₁, x₂, …, x_k is given by the multiple linear regression model

and the estimated response is obtained ...