Answer: At least one of the coefficients is statistically significantly different from zero.

## Explanation The F-statistic is a measure used in statistical analysis to assess the significance of the overall regression model. In the context of a joint hypothesis test, the F-statistic is used to determine whether at least one of the independent variables in the model has a significant effect on the dependent variable. ### Key Points: - **Null Hypothesis**: All coefficients (b₁, b₂, b₃) = 0 - **Alternative Hypothesis**: At least one coefficient ≠ 0 - **F-statistic > Critical F-value**: Reject the null hypothesis ### Interpretation: When the F-statistic exceeds the critical F-value, we reject the null hypothesis that all coefficients are zero. This means **at least one** of the independent variables has a statistically significant effect on the dependent variable. ### Why Other Options Are Incorrect: - **B**: The F-test doesn't guarantee that **each** coefficient is significant - it only tells us that at least one is significant - **C**: If none were significant, the F-statistic would be less than or equal to the critical value - **D**: The F-test cannot determine that **only one** coefficient is significant - it could be one, two, or all three This is a fundamental concept in multiple regression analysis where the F-test assesses the overall model significance, while individual t-tests would be needed to determine which specific coefficients are significant.

Author: Tanishq Prabhu