Hi,

In the below example from GARP 2016 Practice exam, the joint significance of the coefficients of the multiple regression is tested with F statistic, not T stat. Please clarify why F stat is appropriate to use in this case.

For a sample of 400 firms, the relationship between corpor ate revenue (Yi) and the average years of experienceper employee (Xi) is modeled as follows:

Yi= β1+ β2Xi+ εi,i = 1, 2,...,400

You wish to test the joint null hypothesis that β1 = 0 and β2 = 0 at the 95% confidence level. The p-value for the t-statistic for β1 is 0.07 , and the p-value for the t-statistic for β2 is 0.06. The p-value for the F-statistic for the regression is 0.045. Which of the following statements is correct?

a. You can reject the null hypothesis because each β is different from 0 at the 95% confidence level.

b. You cannot reject the null hypothesis because neither β is different from 0 at the 95% confidence level.

c. You can reject the null hypothesis because the F-statistic is significant at the 95% confidence level.

d. You cannot reject the null hypothesis because the F-statistic is not significant at the 95% confidence level.

Explanation: The t-test would not be sufficient to test the joint hypothesis. In order to test the joint null hypothesis, examine the F-statistic, which in this case is statistically significant at the 95% confidence level. Thus the null can be rejected.

In the below example from GARP 2016 Practice exam, the joint significance of the coefficients of the multiple regression is tested with F statistic, not T stat. Please clarify why F stat is appropriate to use in this case.

For a sample of 400 firms, the relationship between corpor ate revenue (Yi) and the average years of experienceper employee (Xi) is modeled as follows:

Yi= β1+ β2Xi+ εi,i = 1, 2,...,400

You wish to test the joint null hypothesis that β1 = 0 and β2 = 0 at the 95% confidence level. The p-value for the t-statistic for β1 is 0.07 , and the p-value for the t-statistic for β2 is 0.06. The p-value for the F-statistic for the regression is 0.045. Which of the following statements is correct?

a. You can reject the null hypothesis because each β is different from 0 at the 95% confidence level.

b. You cannot reject the null hypothesis because neither β is different from 0 at the 95% confidence level.

c. You can reject the null hypothesis because the F-statistic is significant at the 95% confidence level.

d. You cannot reject the null hypothesis because the F-statistic is not significant at the 95% confidence level.

**Correct answer: c**Explanation: The t-test would not be sufficient to test the joint hypothesis. In order to test the joint null hypothesis, examine the F-statistic, which in this case is statistically significant at the 95% confidence level. Thus the null can be rejected.

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