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Answer: Intercept term (a): No; Slope coefficient (b): Yes
## 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.
Author: Tanishq Prabhu
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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.
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
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