Dummy Variables And the Analysis of Covariance

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Dummy Variables And the Analysis of Covariance
William L William Leo White
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See Bryant [11, pp. 21^4-216 or F-razer [3], pp. 296-30^1.
- 5 - SSR(d) = ) (y. . - a. - b x. . ), i. E. , the sum of squared residuals ~'. From a regression with Dummy variables •^ included, with IJ - n - (l - l) degrees of freedom.
It should be clear that SSR(d) measures the unexplained or residual portion of the variation. Also, the combined reduction due to the x's and Z's is SS(y) - SSR(d). Since the reduction due to the inclusion of the x's is SS(y) - SSR(a), the incremental reduction due
... to the inclusion of the Z's, the dummy variables, is [SS(y) - SSR(d)] - [SS(y) - SSR(a)]. That is, it is the reduction due to the combined effects of the x's and the Z's minus the effect of the x's. Simplifying, this becomes SSR(a) - SSR(d). In other words, the contribution of the dummy variables is meas- ured by the difference between the residual sum of squares after the in- clusion of the x's, but before the inclusion of the dummy variables, and the residual sum of squares after the inclusion of both the x's and the dummy variables.

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