Financial Risk Manager Part 1
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A multiple regression model with three variables has the following formula:
A FRM exam candidate performs a joint hypothesis test where:
If the computed -statistic is less than the tabulated one-tailed -value, this implies that:
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NNikitesh
A
All the three coefficients of the independent variables are statistically different from zero
B
Only is statistically different from zero
C
The effects of the independent variables on are statistically significant
D
None of the coefficients are statistically significantly different from zero
Explanation:
In joint hypothesis testing for multiple regression:
- Null Hypothesis (H₀): All coefficients are equal to zero (b₁ = b₂ = b₃ = 0)
- Alternative Hypothesis (H₁): At least one coefficient is statistically different from zero
- F-statistic test:
- If computed F-statistic > critical F-value → Reject H₀ (at least one coefficient is significant)
- If computed F-statistic < critical F-value → Fail to reject H₀ (no evidence that any coefficient is significant)
Since the computed F-statistic is less than the tabulated one-tailed F-value, we fail to reject the null hypothesis. This means there is insufficient evidence to conclude that any of the coefficients (b₁, b₂, or b₃) are statistically significantly different from zero.
Key points:
- The F-test in regression tests the joint significance of all coefficients (except the intercept)
- A low F-statistic indicates the model as a whole is not statistically significant
- This does not mean individual coefficients might not be significant if tested separately, but the joint test fails to reject the null hypothesis that all coefficients are zero
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