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, *x*_{1} denotes the temperature, and *x*_{2} 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 *β*_{0}, *β*_{1} and *β*_{2}.

The regression model in Eq. (3.1) describes a plane in the three-dimensional space of *y*, *x*_{1} and *x*_{2}. Figure 3.1*a* 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 *β*_{0} is the intercept of the regression plane. If the range of the data includes *x*_{1} = *x*_{2} = 0, then *β*_{0} is the mean of *y* when *x*_{1} = *x*_{2} = 0. Otherwise *β*_{0} has no physical interpretation. The parameter *β*_{1} indicates the expected change in response(*y*) per unit change in ...

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