Precision Or Standard Errors Of Leastsquares Estimates

From Eqs. (3.1.6) and (3.1.7), it is evident that least-squares estimates are a function of the sample data. But since the data are likely to change from sample to sample, the estimates will change ipso facto. Therefore, what is needed is some measure of "reliability" or precision of the estimators jj1 and j2. In statistics the precision of an estimate is measured by its standard error (se).17 Given the Gaussian assumptions, it is shown in Appendix 3A, Section 3A.3 that the standard errors of the OLS estimates can be obtained

16Mark Blaug, The Methodology of Economics: Or How Economists Explain, 2d ed., Cambridge University Press, New York, 1992, p. 92.

17The standard error is nothing but the standard deviation of the sampling distribution of the estimator, and the sampling distribution of an estimator is simply a probability or frequency distribution of the estimator, that is, a distribution of the set of values of the estimator obtained from all possible samples of the same size from a given population. Sampling distributions are used to draw inferences about the values of the population parameters on the basis of the values of the estimators calculated from one or more samples. (For details, see App. A.)

CHAPTER THREE: TWO-VARIABLE REGRESSION MODEL 77

as follows:

var (¿2) =

e x2

se (¿2) =

a

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