The correct relationship between SST, SSR, and SSE is given by
A) SSR = SST + SSE.
B) SSR = SST - SSE.
C) SSE = SSR + SST.
D) n(SST) = p(SSR) + (n - p)(SSE).

Question

Quizplus · Accepted Answer

The best relationship among SST, SSR, and SSE is given by B) SSR = SST -SSE.

SST (Total sum of squares) represents the total variation of the data. It is the sum of the squared differences between the observed dependent variable and the mean of the dependent variable.

SSR (Regression sum of squares) represents the variation that is explained by the regression model. It is the sum of the squared differences between the predicted values of the dependent variable and the mean of the dependent variable.

SSE (Error sum of squares) represents the unexplained variation by the regression model. It is the sum of the squared differences between the observed dependent variable and the predicted values of the dependent variable.

Therefore, the best relationship between these three is given by SSR = SST - SSE because it shows that the total sum of squares (SST) can be decomposed into two components: the sum of squares due to regression (SSR) and the sum of squares due to error (SSE).

The Correct Relationship Between SST, SSR, and SSE Is Given