Question

In a multiple regression model involving 44 observations, the following estimated regression equation was obtained. Ŷ = 29 + 18x1 + 43x2 + 87x3 For this model, SSR = 600 and SSE = 400. The multiple coefficient of determination for the above model is
A. .600.
B. .667.
C. .336.
D. .400.

Answer 1

Answer: D. .400

Step-by-step explanation:

Given : In a multiple regression model involving 44 observations, the following estimated regression equation was obtained.

$\hat{Y}= 29 + 18x_1 + 43x_2 + 87x_3$

For this model,

Regression sum of squares =SSR = 600

and Sum of squares due to error =SSE = 400.

Total sum of squares = SST= SSR+SSE

SST= 600+400=1000

The multiple coefficient of determination is given by :-

$R^2=1-\dfrac{SSR}{SST}$

Substitute values , we get

$R^2=1-\dfrac{600}{1000}$

$R^2=1-0.600=0.400$

Thus, the multiple coefficient of determination for the above model is $R^2=0.400$

Hence, the correct answer is D. .400.