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.
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 ...