The important topics and concepts developed in this chapter can be summarized as follows.
1. The basic framework of regression analysis is the CLRM.
3. Based on these assumptions, the least-squares estimators take on certain properties summarized in the Gauss-Markov theorem, which states that in the class of linear unbiased estimators, the least-squares estimators have minimum variance. In short, they are BLUE.
4. The precision of OLS estimators is measured by their standard errors. In Chapters 4 and 5 we shall see how the standard errors enable one to draw inferences on the population parameters, the facoefficients.
5. The overall goodness of fit of the regression model is measured by the coefficient of determination, r2. It tells what proportion of the variation in the dependent variable, or regressand, is explained by the explanatory variable, or regressor. This r2 lies between 0 and 1; the closer it is to 1, the better is the fit.
6. A concept related to the coefficient of determination is the coefficient of correlation, r. It is a measure of linear association between two variables and it lies between -1 and +1.
7. The CLRM is a theoretical construct or abstraction because it is based on a set of assumptions that may be stringent or "unrealistic." But such abstraction is often necessary in the initial stages of studying any field of knowledge. Once the CLRM is mastered, one can find out what happens if one or more of its assumptions are not satisfied. The first part of this book is devoted to studying the CLRM. The other parts of the book consider the refinements of the CLRM. Table 3.4 gives the road map ahead.
Type of violation
Where to study?
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