Category Springer Texts in Business and Economics

A Measure of Fit

We have obtained the least squares estimates of a, в and a2 and found their distributions under normality of the disturbances. We have also learned how to test hypotheses regarding these parameters. Now we turn to a measure of fit for this estimated regression line. Recall, that ei = Yi — YPi where YPi denotes the predicted Yi from the least squares regression line at the value Xi, i. e., aoLS + POLSXi. Using the fact that £i=1 ei = 0, we deduce that £П= Yi = £П=1 Yi,

and therefore, Y = Y. The actual and predicted values of Y have the same sample mean, see numerical properties (i) and (iii) of the OLS estimators discussed in section 2. This is true

as long as there is a constant in the regression. Adding and subtracting Y from ti, we get ei = yi — yi, or yi = ei + y...

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