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Nonlinear Regression Functions 303

Figure 8.1 Population Regression Functions with Different Slopes

YY

Rise Rise
Run
Run
(a) Constant slope X1
Population regression Rise
Y function when X2 = 1 Run

Rise X1
Run (b) Slope depends on the value of X1

Rise
Run

Population regression function when X2 = 0

X1
(c) Slope depends on the value of X2

In Figure 8.1a, the population regression function has a constant slope. In Figure 8.1b, the slope of the population
regression function depends on the value of X1. In Figure 8.1c, the slope of the population regression function
depends on the value of X2.

(or parameters) of the population regression model and thus are versions of the
multiple regression model of Chapters 6 and 7. Therefore, the unknown parameters
of these nonlinear regression functions can be estimated and tested using OLS and
the methods of Chapters 6 and 7.

Sections 8.1 and 8.2 introduce nonlinear regression functions in the context of
regression with a single independent variable, and Section 8.3 extends this to two
independent variables. To keep things simple, additional control variables are
omitted in the empirical examples of Sections 8.1 through 8.3. In practice, however,
it is important to analyze nonlinear regression functions in models that control for
omitted factors by including control variables as well. In Section 8.5, we combine
nonlinear regression functions and additional control variables when we take a close