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 | df | SS |
|---|---|---|
| Regression | 2 | 240 |
| Residual | 37 | 1070 |
| Total | 39 | 1300 |
| Multiple R | 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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NNikitesh
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:
The F-test is used to test the overall significance of a regression model. It tests the null hypothesis that all slope coefficients are equal to zero against the alternative hypothesis that at least one slope coefficient is not equal to zero. This is different from t-tests, which test individual coefficients. The ANOVA table provided in the question is specifically used for conducting the F-test, where the F-statistic is calculated as (Regression SS/Regression df) / (Residual SS/Residual df). The correct formulation is: H₀: All slope coefficients = 0; Hₐ: At least one slope coefficient ≠ 0.
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