Exhibit 15-7
A regression model involving 4 independent variables and a sample of 15 periods resulted in the following sum of squares.
SSR = 165
SSE = 60
-Refer to Exhibit 15-7. If we want to test for the significance of the model at 95% confidence, the critical F value (from the table) is
A)3.06
B)3.48
C)3.34
D)3.11

Question

Quizplus · Accepted Answer

To test for the significance of the model, we need to perform an F-test with the following hypotheses: 
H0: β1 = β2 = β3 = β4 = 0 (the model has no explanatory power)
Ha: at least one βi is not equal to 0 (the model has explanatory power)
Under the null hypothesis, the expected value of SSR divided by its degrees of freedom (4) is equal to the expected value of SSE divided by its degrees of freedom (n-5=10) which is the error variance (σ2). In other words, SSR/4 and SSE/10 should be about the same. If the model has no explanatory power, then any variation in the dependent variable is due to random error, and the R-squared should be close to 0. Therefore, we can compute the F-statistic as follows:
F = (SSR/4) / (SSE/10) ≈ R2/(1-R2) * (n-5)/4 ~ F(4,10)
where R2 = 1 - SSE/TSS and TSS is the total sum of squares, which can be expressed as TSS = SSR + SSE. 
Plugging in the numbers from the exhibit, we get:
F = (165/4) / (60/10) ≈ 0.69 * 2 = 1.38
To find the critical F-value from the table with α=0.05 and (df1=4, df2=10), we look at the intersection of the row for df1=4 and the column for df2=10, which gives us Fcrit = 3.48.
Since our computed F (1.38) is smaller than the critical F (3.48), we fail to reject the null hypothesis and conclude that the model is not significant at the 95% confidence level.

Exhibit 15-7 A Regression Model Involving 4 Independent Variables and a Sample