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 30 years. The NIFTY is the National Stock Exchange (NSE) index in India. The results are as shown below. Regression equation:
R_index, t = â + b̂ × R_stock, t + ε_t
| 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? Click here to see critical values of the t-distribution._
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TTanishq
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 the regression coefficients are statistically different from zero at a 95% confidence level, we perform t-tests for each coefficient.
Hypothesis Tests:
- For intercept (a): H₀: a = 0 vs. H₁: a ≠ 0
- For slope (b): H₀: b = 0 vs. H₁: b ≠ 0
Degrees of Freedom:
- n = 30 years
- Degrees of freedom = n - 2 = 30 - 2 = 28
Critical Value:
- For a 95% confidence level (5% significance level, two-tailed)
- Critical t-value = 2.048
Test Statistics:
For intercept (a):
- t-statistic = (0.002 - 0) / 0.001 = 2.0
- Since |2.0| < 2.048, we fail to reject H₀
- Conclusion: Intercept is not statistically significant
For slope (b):
- t-statistic = (1.223 - 0) / 0.063 = 19.413
- Since |19.413| > 2.048, we reject H₀
- Conclusion: Slope is statistically significant
Final Interpretation:
- Intercept term (a): No (not statistically different from zero)
- Slope coefficient (b): Yes (statistically different from zero)
This matches option C.
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