Financial Risk Manager Part 1
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An analyst has regressed the annual return on a stock (R_stock) against the annual return on the NIFTY 50 (R_index) for 36 years. The NIFTY is the National Stock Exchange (NSE) index in India. The results are as shown below.
Regression equation:
| Coefficient | Coefficient Estimate | Standard Error |
|---|---|---|
| a | 0.002 | 0.001 |
| b | 1.223 | 0.063 |
Interpret whether the regression coefficients are statistically different from zero at a 95% confidence level?
Other
Community
NNikitesh
A
Intercept term (a): Yes; Slope coefficient (b): Yes
B
Intercept term (a): No; Slope coefficient (b): No
C
Intercept term (a): No; Slope coefficient (b): Yes
D
Intercept term (a): Yes; Slope coefficient (b): No
Explanation:
Explanation:
To determine if regression coefficients are statistically different from zero at 95% confidence level, we perform t-tests:
1. Hypotheses:
- For intercept (a): H₀: a = 0 vs. H₁: a ≠ 0
- For slope (b): H₀: b = 0 vs. H₁: b ≠ 0
2. Degrees of freedom: n - 2 = 36 - 2 = 34
3. Critical t-value: For 34 degrees of freedom at 95% confidence level (2-tailed, α = 0.05), the critical t-value is approximately 2.03.
4. Test statistics calculation:
- For intercept: t = (0.002 - 0) / 0.001 = 2.0
- For slope: t = (1.223 - 0) / 0.063 = 19.413
5. Decision rule: Reject H₀ if |t-statistic| > critical t-value (2.03)
6. Results:
- Intercept: t = 2.0 < 2.03 → Fail to reject H₀ → Intercept is NOT statistically significant
- Slope: t = 19.413 > 2.03 → Reject H₀ → Slope IS statistically significant
Therefore, the intercept term is not statistically different from zero, while the slope coefficient is statistically different from zero at the 95% confidence level.
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