For a multiple regression model the following statistics are given: Total SS = 400, SSR = 350, k = 4, and n = 20. The coefficient of determination adjusted for degrees of freedom is:
A) 87.5%
B) 15.83%
C) 12.5%
D) 84.17%
E) 16.54%

Question

Quizplus · Accepted Answer

The coefficient of determination (R-squared) is given by the ratio SSR/Total SS.

So, R-squared = SSR/Total SS = 350/400 = 0.875

The adjusted R-squared formula takes into account the number of predictors and the sample size:

Adjusted R-squared = 1 - [(1 - R-squared)(n - 1)/(n - k - 1)]

Plugging in the numbers:

Adjusted R-squared = 1 - [(1 - 0.875)(20 - 1)/(20 - 4 - 1)] = 0.8417 or 84.17%

Therefore, the answer is D.

For a Multiple Regression Model the Following Statistics Are Given