Econometria

Gujarati: Basic Econometrics, Fourth Edition

I. Single−Equation Regression Models

7. Multiple Regression Analysis: The Problem of Estimation

© The McGraw−Hill Companies, 2004

7
MULTIPLE REGRESSION ANALYSIS: THE PROBLEM OF ESTIMATION

The two-variable model studied extensively in the previous chapters is often inadequate in practice. In our consumption–income example, for instance, it was assumed implicitly that only income X affects consumption Y. But economic theory is seldom so simple for, besides income, a number of other variables are also likely to affect consumption expenditure. An obvious example is wealth of the consumer. As another example, the demand for a commodity is likely to depend not only on its own price but also on the prices of other competing or complementary goods, income of the consumer, social status, etc. Therefore, we need to extend our simple two-variable regression model to cover models involving more than two variables. Adding more variables leads us to the discussion of multiple regression models, that is, models in which the dependent variable, or regressand, Y depends on two or more explanatory variables, or regressors. The simplest possible multiple regression model is three-variable regression, with one dependent variable and two explanatory variables. In this and the next chapter we shall study this model. Throughout, we are concerned with multiple linear regression models, that is, models linear in the parameters; they may or may not be linear in the variables.
7.1 THE THREE-VARIABLE MODEL: NOTATION AND ASSUMPTIONS

Generalizing the two-variable population regression function (PRF) (2.4.2), we may write the three-variable PRF as Yi = β1 + β2 X2i + β3 X3i + ui
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(7.1.1)

Gujarati: Basic Econometrics, Fourth Edition

I. Single−Equation Regression Models

7. Multiple Regression Analysis: The Problem of Estimation

© The McGraw−Hill Companies, 2004

CHAPTER SEVEN: MULTIPLE REGRESSION ANALYSIS: THE