Y2 E y2 E U yu E y2 e U 2 e e u

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.

Was this article helpful?

0 0
Rules Of The Rich And Wealthy

Rules Of The Rich And Wealthy

Learning About The Rules Of The Rich And Wealthy Can Have Amazing Benefits For Your Life And Success. Discover the hidden rules and beat the rich at their own game. The general population has a love / hate kinship with riches. They resent those who have it, but spend their total lives attempting to get it for themselves. The reason an immense majority of individuals never accumulate a substantial savings is because they don't comprehend the nature of money or how it works.

Get My Free Ebook


Post a comment