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Answer: You can reject the null hypothesis because the F-statistic is significant at the 95% confidence level.
## Explanation For testing the joint null hypothesis that β₁ = 0 and β₂ = 0, we use the F-statistic rather than individual t-tests. **Key points:** - **Individual t-tests:** p-values are 0.07 and 0.06, both > 0.05, so we cannot reject individual null hypotheses at 95% confidence level - **F-test for joint hypothesis:** p-value = 0.045 < 0.05, so we CAN reject the joint null hypothesis at 95% confidence level **Why this happens:** - The F-test considers the joint significance of multiple coefficients simultaneously - Even when individual coefficients are not statistically significant, their combined effect might be significant - This is common in regression analysis where variables may be correlated **Correct answer:** C - We can reject the null hypothesis because the F-statistic is significant at the 95% confidence level.
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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.
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