Financial Risk Manager Part 1
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In a hypothetical world, GDP is regressed against interest rate and inflation, and regression results are shown below.
GDP = a + b (Interest rate) + c (Inflation) + Error term
| Coefficient | p-Value |
|---|---|
| a | 9 |
| b | 2 |
| c | 1.5 |
ANOVA Table:
| Source | df | SS |
|---|---|---|
| Regression | 2 | 240 |
| Residual | 37 | 1070 |
| Total | 39 | 1300 |
| Total | — | 0.428 |
| R2 | — | 0.183 |
| Observation | 40 | — |
Which of the test is relevant to determine whether the regression model as a whole is significant?
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A
F – test; H₀: All slope coefficients = 0; Hₐ: At least one slope coefficient ≠ 0
B
F – test; H₀: All slope coefficients ≥ 0; Hₐ: At least one slope coefficient < 0
C
t – test; H₀: All slope coefficients = 0; Hₐ: At least one slope coefficient ≠ 0
D
t – test; H₀: All slope coefficients ≥ 0; Hₐ: At least one slope coefficient < 0
Explanation:
Explanation
An F-test is used to test whether any of the independent variables explain the variation in the dependent variable (test of overall model significance). It is used to determine whether the regression model as a whole is significant.
Key Points:
- F-test assesses the overall significance of the regression model
- Null Hypothesis (H₀): All slope coefficients = 0 (no relationship between independent variables and dependent variable)
- Alternative Hypothesis (Hₐ): At least one slope coefficient ≠ 0 (at least one independent variable has a significant relationship with the dependent variable)
Why not other options:
- Option B: Incorrect hypothesis formulation - F-test doesn't test for coefficients being ≥ 0
- Option C: t-test is used for individual coefficient significance, not overall model significance
- Option D: t-test with incorrect hypothesis formulation
The ANOVA table provided in the question is specifically used to calculate the F-statistic for testing overall model significance.
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