The various sums of squares appearing in (3.5.2) can be described as follows: Y. Ji =J2(Y — Y)2 = total variation of the actual Y values about their sample mean, which may be called the total sum of squares (TSS). e y2 = T,(Yi — Y)2 = Y(Yi — Y)2 = ^ e xf = variation of the estimated Y values about their mean (Y = Y), which appropriately may be called the sum of squares due to regression [i.e., due to the explanatory variable(s)], or explained by regression, or simply the explained sum of squares (ESS). Y u2 = residual or unexplained variation of the Y values about the regression line, or simply the residual sum of squares (RSS). Thus, (3.5.2) is and shows that the total variation in the observed Y values about their mean value can be partitioned into two parts, one attributable to the regression line and the other to random forces because not all actual Y observations lie on the fitted line. Geometrically, we have Figure 3.10.
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