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.