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Answer: Intercept term (a): No; Slope coefficient (b): Yes
**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.
Author: Nikitesh Somanthe
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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?
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