Consider the regression models described in Example 8.4.

Example 8.4

a. Graph the response function associated with Eq. (8.10).

Equation  (8.10)

b. Graph the response function associated with Eq. (8.11).

Equation (8.11)

Frequently there are several different qualitative variables that must be incorpo- rated into the model. To illustrate, suppose that in Example 8.1 a second qualitative factor, the type of cutting oil used, must be considered. Assuming that this factor has two levels, we may define a second indicator variable, X3, as follows: X3 (0 if low-viscosity oil used [1 if medium-viscosity oil used A regression model relating tool life (y) to cutting speed (x1), tool type (x2), and type of cutting oil (x3) is y= Bo+B1x1 + B2x2 +3x3 + (8.9) Clearly the slope of the regression model relating tool life to cutting speed does not depend on either the type of tool or the type of cutting oil. The intercept of the regression line depends on these factors in an additive fashion.