In a regression model involving 30 observations, the following estimated regression model was obtained: $\hat { y }$ = 60 + 2.8x1 + 1.2 x2 - x3. For this model, total variation in y = SST = 800 and SSE = 200. The value of the F-statistic for testing the validity of this model is:
A)26.00.
B)7.69.
C)3.38.
D)0.039.

Question

Quizplus · Accepted Answer

The F-statistic is calculated as $ F = \frac{MSR}{MSE} $, where $ MSR = \frac{SSR}{k} $ and $ MSE = \frac{SSE}{n-k-1} $. Here, $ SSR = SST - SSE = 800 - 200 = 600 $, $ k = 3 $, and $ n = 30 $. Thus, $ MSR = \frac{600}{3} = 200 $ and $ MSE = \frac{200}{26} \approx 7.69 $. Therefore, $ F = \frac{200}{7.69} \approx 26.00 $.

In a Regression Model Involving 30 Observations, the Following Estimated y^\hat { y }y^​

In a Regression Model Involving 30 Observations, the Following Estimated $\hat { y }$