Financial Risk Manager Part 1
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A multiple regression model has 4 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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NNikitesh
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:
A joint hypothesis test is used to assess whether at least one of the independent variables explains a significant portion of the total variation exhibited by the dependent variable. To determine the statistical significance, the F-statistic calculated is compared with the always one-tailed critical F-value. The null hypothesis is rejected when the F-statistic > one-tailed critical value, indicating that at least one of the coefficients is statistically significantly different from zero.
Key Points:
- The joint hypothesis test (F-test) tests the null hypothesis that all coefficients are equal to zero: H₀: β₁ = β₂ = β₃ = 0
- When the F-statistic exceeds the critical F-value, we reject the null hypothesis
- Rejection of the null hypothesis means that at least one coefficient is statistically different from zero, but it doesn't tell us which ones or how many
- Option B is incorrect because the F-test doesn't guarantee that ALL coefficients are significant - it only indicates that at least one is
- Option C is incorrect because we reject the null hypothesis
- Option D is incorrect because we cannot conclude that only one coefficient is significant from the F-test alone
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