Explanation

To determine which hypotheses can be rejected at a 5% significance level, we need to examine the p-values associated with each coefficient test:

• Hypothesis I ($H_0: B_0 = 0$): The intercept coefficient $B_0$ has a p-value of 0.0000, which is less than 0.05. Therefore, we can reject the null hypothesis that $B_0 = 0$.

• Hypothesis II ($H_0: B_1 = 0$): The coefficient $B_1$ has a p-value of 0.0513, which is greater than 0.05. Therefore, we cannot reject the null hypothesis that $B_1 = 0$.

• Hypothesis III ($H_0: B_2 = 0$): The coefficient $B_2$ has a p-value of 0.0000, which is less than 0.05. Therefore, we can reject the null hypothesis that $B_2 = 0$.

• Hypothesis IV ($H_0: B_1 = B_2 = 0$): This is a joint hypothesis test. The F-statistic has a p-value of 0.0000, which is less than 0.05. Therefore, we can reject the joint null hypothesis that both $B_1$ and $B_2$ equal zero.

Summary of rejections:

• I: ✓ Rejected (p-value = 0.0000 < 0.05)
• II: ✗ Not rejected (p-value = 0.0513 > 0.05)
• III: ✓ Rejected (p-value = 0.0000 < 0.05)
• IV: ✓ Rejected (p-value = 0.0000 < 0.05)

Therefore, hypotheses I, III, and IV can be rejected, which corresponds to Option D.