For a multiple regression model, the following statistics are given: Total variation in y = SST = 250, SSE = 50, k = 4, n = 20.
The coefficient of determination adjusted for degrees of freedom is:
A)0.800.
B)0.747.
C)0.840.
D)0.775.

Question

Quizplus · Accepted Answer

The formula for the adjusted coefficient of determination is:
$R^2_{adj} = 1 - \frac{SSE/(n-k-1)}{SST/(n-1)}$
Plugging in the given values, we get:
$R^2_{adj} = 1 - \frac{50/(20-4-1)}{250/(20-1)} = 1 - \frac{5}{18} = 0.722$
Therefore, the closest choice is B) 0.747, which is the closest rounded value.

For a Multiple Regression Model, the Following Statistics Are Given