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 |
Other statistics:
- Multiple R: 0.428
- R²: 0.183
- Observation: 40
Assume that on a certain significance level, the critical value of the F-statistic is 4. Which of the following is correct?
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NNikitesh
A
The value of F-statistic is less than its critical value
B
We fail to reject the null hypothesis: H₀: All slope coefficients = 0
C
The model as a whole is statistically significant
D
The model as whole is not statistically significant
Explanation:
Calculation of F-statistic:
F = (RSS/k) / (SSE/(n-k-1))
Where:
- RSS (Regression Sum of Squares) = 240
- k (number of independent variables) = 2
- SSE (Sum of Squared Errors/Residuals) = 1070
- n (number of observations) = 40
F = (240/2) / (1070/(40-2-1)) = 120 / (1070/37) = 120 / 28.9189 = 4.1495
Decision Rule:
- F-statistic (4.1495) > Critical value (4)
- Since F-statistic > critical value, we reject the null hypothesis H₀: All slope coefficients = 0
- This means the model as a whole is statistically significant
Analysis of Options:
- A: Incorrect - F-statistic (4.1495) is greater than critical value (4)
- B: Incorrect - We reject the null hypothesis, not fail to reject
- C: Correct - Model is statistically significant since we reject H₀
- D: Incorrect - Opposite of the correct conclusion
Additional Notes:
- The p-values for individual coefficients (b: 0.035, c: 0.012) also suggest they are statistically significant at conventional levels
- R² of 0.183 indicates about 18.3% of GDP variation is explained by the model
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