multiple regression analysis

In Chapter 2, we learned how to use simple regression analysis to explain a dependent
variable, y, as a function of a single independent variable, x. The primary drawback
in using simple regression analysis for empirical work is that it is very difficult
to draw ceteris paribus conclusions about how x affects y: the key assumption,
SLR.3—that all other factors affecting y are uncorrelated with x—is often unrealistic.
Multiple regression analysis is more amenable to ceteris paribus analysis because it
allows us to explicitly control for many other factors which simultaneously affect the
dependent variable. This is important both for testing economic theories and for evaluating
policy effects when we must rely on nonexperimental data. Because multiple regression
models can accommodate many explanatory variables that may be correlated, we can
hope to infer causality in cases where simple regression analysis would be misleading.
Naturally, if we add more factors to our model that are useful for explaining y, then
more of the variation in y can be explained. Thus, multiple regression analysis can be
used to build better models for predicting the dependent variable.
An additional advantage of multiple regression analysis is that it can incorporate
fairly general functional form relationships. In the simple regression model, only one
function of a single explanatory variable can appear in the equation. As we will see, the
multiple regression model allows for much more flexibility.
Section 3.1 formally introduces the multiple regression model and further discusses
the advantages of multiple regression over simple regression. In Section 3.2, we
demonstrate how to estimate the parameters in the multiple regression model using the
method of ordinary least squares. In Sections 3.3, 3.4, and 3.5, we describe various statistical
properties of the OLS estimators, including unbiasedness and efficiency.
The multiple regression model is still the most widely used vehicle for empirical
analysis in economics and other social sciences. Likewise, the method of ordinary least
squares is popularly used for estimating the parameters of the multiple regression model.
3.1 MOTIVATION FOR MULTIPLE REGRESSION
The Model with Two Independent Variables
We begin with some simple examples to show how multiple regression analysis can be
used to solve problems that cannot be solved by simple regression.

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