Refer to the portion of regression results in the accompanying table. When testing the overall significance of the regression model at the 5% level given a critical value of F_{0.05, (2.20)} = 3.49,the decision is to _____________________________________________________________. A) reject H₀ and conclude that the explanatory variables are jointly significant. B) not reject H₀ and conclude that the explanatory variables are jointly significant. C) reject H₀ and conclude that the explanatory variables are not jointly significant. D) not reject H₀ and conclude that the explanatory variables are not jointly significant.

Question

Quizplus · Accepted Answer

To determine if the regression model as a whole has statistical significance, we need to test the null hypothesis:

H0: β1= β2 = β3 = 0

versus the alternative hypothesis:

HA: At least one βj ≠ 0

where β1, β2, and β3 are the regression coefficients for the three explanatory variables.

To perform this test, we can use the F-statistic:

F = MSR / MSE

where MSR is the regression mean square and MSE is the error mean square, both of which are provided in the ANOVA table.

Under the null hypothesis, the F-statistic follows an F-distribution with degrees of freedom d1 = k (the number of regressors) and d2 = n - k - 1 (the number of observations minus the number of regressors minus one). In this case, we have k = 3 and n = 40, so d1 = 3 and d2 = 36.

The critical value of F at the 5% level of significance is obtained from the F-distribution table with d1 = 3 and d2 = 36. The table value is approximately 2.87.

Comparing the calculated F-value of 3.49 to the critical F-value of 2.87, we see that F > F_critical. Therefore, we reject the null hypothesis and conclude that the regression model as a whole is statistically significant at the 5% level.

In other words, we can say that the explanatory variables (age, education, and experience) are jointly significant in explaining the response variable (salary). The correct choice is A.

Refer to the Portion of Regression Results in the Accompanying