A regression model involving 4 independent variables and a sample of 15 observations resulted in the following sum of squares. SSR = 165
SSE = 60

The multiple coefficient of determination is
A) .3636.
B) .7333.
C) .275.
D) .5.

Question

A regression model involving 4 independent variables and a sample of 15 observations resulted in the following sum of squares. SSR = 165
SSE = 60
​
The multiple coefficient of determination is
A) .3636.
B) .7333.
C) .275.
D) .5.

Quizplus · Accepted Answer

The total sum of squares (SST) can be calculated as SST = SSR + SSE. We do not have the value of SST given, so we cannot calculate the multiple coefficient of determination directly. However, we know that the multiple coefficient of determination (R-squared) is given by SSR/SST. Thus, we need to find SST.

SST = SSR + SSE = 165 + 60 = 225

Therefore, R-squared = SSR/SST = 165/225 = 0.7333, or approximately 0.73.

So the best choice is B with the explanation that it is calculated using the formula R-squared = SSR/SST, where SST = SSR + SSE, and SST is not given in the problem, so we first need to calculate it as SST = SSR + SSE = 165 + 60 = 225.

A Regression Model Involving 4 Independent Variables and a Sample