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

## Explanation This question involves testing a joint null hypothesis using both individual t-tests and an F-test: ### Key Information: - **Joint null hypothesis**: β₁ = 0 and β₂ = 0 - **Confidence level**: 95% (α = 0.05) - **Individual p-values**: - β₁: p-value = 0.07 - β₂: p-value = 0.06 - **F-statistic p-value**: 0.045 ### Analysis: 1. **Individual t-tests**: - For β₁: p-value = 0.07 > 0.05 → Cannot reject H₀: β₁ = 0 - For β₂: p-value = 0.06 > 0.05 → Cannot reject H₀: β₂ = 0 - Therefore, neither coefficient is individually significant at the 95% confidence level 2. **F-test for joint hypothesis**: - p-value = 0.045 < 0.05 → Can reject the joint null hypothesis H₀: β₁ = β₂ = 0 - The F-test examines whether at least one of the coefficients is significantly different from zero ### Why Option C is Correct: - The F-statistic p-value (0.045) is less than the significance level (0.05), so we can reject the joint null hypothesis - This means that at least one of the coefficients (β₁ or β₂) is significantly different from zero - The F-test is more powerful for testing joint hypotheses than individual t-tests ### Why Other Options are Incorrect: - **A**: Incorrect because neither β is individually significant (both p-values > 0.05) - **B**: Incorrect because the F-test allows us to reject the joint null hypothesis - **D**: Incorrect because the F-statistic IS significant (p-value = 0.045 < 0.05) This demonstrates the important distinction between individual coefficient tests and joint hypothesis testing in regression analysis.

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