In regression analysis, the total variation in the dependent variable y, measured by , can be decomposed into two parts: the explained variation, measured by SSR, and the unexplained variation, measured by SSE.

Question

In regression analysis, the total variation in the dependent variable y, measured by  , can be decomposed into two parts: the explained variation, measured by SSR, and the unexplained variation, measured by SSE.

Quizplus · Accepted Answer

This is true, as the total sum of squares (TSS) can be decomposed into the explained sum of squares (ESS) and the residual sum of squares (RSS). Another way to express this is TSS = ESS + RSS, where ESS is the sum of the squared differences between the predicted y-values and the mean of y, and RSS is the sum of the squared differences between the actual y-values and the predicted y-values. Therefore, SSR (sum of squares due to regression) is equivalent to ESS, while SSE (sum of squares error) is equivalent to RSS.

In Regression Analysis, the Total Variation in the Dependent Variable