Financial Risk Manager Part 1
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A multiple regression model has 3 independent variables such that:
An analyst carries out a joint hypothesis test to determine the statistical significance of the independent variable coefficients, incorporating all the 3 variables. The null hypothesis is such that each variable coefficient is equated to zero. The results reveal that the F-statistic is greater than the one-tailed critical F-value. This implies that:
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A
At least one of the coefficients is statistically significantly different from zero.
B
Each of the independent variable coefficients is statistically significantly different from zero.
C
None of the coefficients is statistically different from zero.
D
Only one of the independent variable coefficients is statistically different from zero.
Explanation:
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.
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