## LEAST SQUARES ESTIMATORS

In this section we study the estimation of the parameters a, (3, and a2 in the bivariate linear regression model (10.1.1). We first consider estimating a and (3. The T observations on у and x can be plotted in a so-called scatter diagram, as in Figure 10.1. In that figure each dot represents a vector of observations on у and x. We have labeled one dot as the vector (yt, xt). We have also drawn a straight line through the scattered dots and labeled the point of intersection between the line and the dashed perpendicular line that goes through (yt, xt) as {% xt). Then the problem of estimating a and (3 can be geometrically interpreted as the problem of drawing a straight line such that its slope is an estimate of 3 and its intercept is an estimate of a.

Since Eut = 0, a re...

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