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Answer: The slope coefficient is statistically significant, but the intercept coefficient is not.
## Explanation To determine statistical significance at a 95% confidence level, we perform t-tests for each coefficient using the formula: $$T = \frac{\text{Coefficient estimate} - 0}{\text{Standard error}}$$ ### Slope Coefficient (β₁) Test: - Coefficient estimate: 1.2631 - Standard error: 0.0428 - Test statistic: $$T = \frac{1.2631 - 0}{0.0428} = 29.51$$ ### Intercept Coefficient (β₀) Test: - Coefficient estimate: -0.0178 - Standard error: 0.0139 - Test statistic: $$T = \frac{-0.0178 - 0}{0.0139} = -1.28$$ ### Critical Value: - For a 95% confidence level (two-tailed test), the critical value from the standard normal distribution is ±1.96 ### Decision: - **Slope coefficient (β₁)**: |29.51| > 1.96 → Statistically significant - **Intercept coefficient (β₀)**: |-1.28| < 1.96 → Not statistically significant Therefore, only the slope coefficient is statistically significant at the 95% confidence level, while the intercept coefficient is not statistically different from zero.
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A market risk manager is analyzing the performance of VTFX, a large cap growth mutual fund that uses the performance of the MSCI World Large Cap Growth Index (MWG) as a benchmark. The manager runs a regression using monthly returns of VTFX as the dependent variable and monthly returns of the MWG as the explanatory variable. The constructed regression model and the results of the regression are as follows:
| Coefficient | Coefficient estimate | Standard error |
|---|---|---|
$0.0139$ | ||
$1.2631$ | $0.0428$ | |
| Source of variation | Sum of squares | |
| Explained | $0.0527$ | |
| Residual | $0.0091$ |
At a 95% confidence level, which of the following conclusions would be correct for the manager to make?
A
Both the slope coefficient and the intercept coefficient are not statistically significant.
B
Both the slope coefficient and the intercept coefficient are statistically significant.
C
The intercept coefficient is statistically significant, but the slope coefficient is not.
D
The slope coefficient is statistically significant, but the intercept coefficient is not.
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