Introduction to Linear Regression Analysis, 5th Edition

CHAPTER 3

MULTIPLE LINEAR REGRESSION

A regression model that involves more than one regressor variable is called a multiple regression model. Fitting and analyzing these models is discussed in this chapter. The results are extensions of those in Chapter 2 for simple linear regression.

3.1 MULTIPLE REGRESSION MODELS

Suppose that the yield in pounds of conversion in a chemical process depends on temperature and the catalyst concentration. A multiple regression model that might describe this relationship is

where y denotes the yield, x₁ denotes the temperature, and x₂ denotes the catalyst concentration. This is a multiple linear regression model with two regressor variables. The term linear is used because Eq. (3.1) is a linear function of the unknown parameters β₀, β₁ and β₂.

The regression model in Eq. (3.1) describes a plane in the three-dimensional space of y, x₁ and x₂. Figure 3.1a shows this regression plane for the model

where we have assumed that the expected value of the error term ε in Eq. (3.1) is zero. The parameter β₀ is the intercept of the regression plane. If the range of the data includes x₁ = x₂ = 0, then β₀ is the mean of y when x₁ = x₂ = 0. Otherwise β₀ has no physical interpretation. The parameter β₁ indicates the expected change in response(y) per unit change in ...