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

Question

Quizplus · Accepted Answer

The coefficient of determination is given by R² = SSR/SS. So, R² = 350/400 = 0.875 or 87.5%.

To adjust for degrees of freedom, we use the formula R_adj² = 1 - ((n-1)/(n-k-1))(1-R²).

Plugging in the given values, we get:
R_adj² = 1 - ((20-1)/(20-4-1))(1-0.875) = 0.8417 or 84.17%

Therefore, the best choice is B.

For a Multiple Regression Model the Following Statistics Are Given