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Answer: The slope coefficient is statistically significant, but the intercept coefficient is not.
The correct answer to the question is D. This conclusion is drawn from the results of a regression analysis performed by a market risk manager on the mutual fund VTFX, using the MSCI World Large Cap Growth Index (MWG) as a benchmark. The regression model is given as VTFXt = β0 + β1(MWG) + Et, where β0 is the intercept and β1 is the slope coefficient. The t-test is used to determine the statistical significance of the coefficients. The test statistic for the slope coefficient (β1) is calculated as (1.2631 - 0) / 0.0428, which equals 29.51. This value is compared to the critical value from a standard normal distribution at a 95% confidence level, which is 1.96. Since 29.51 is significantly greater than 1.96, the slope coefficient is statistically significant, indicating that there is a strong relationship between the returns of VTFX and the MWG. On the other hand, the test statistic for the intercept coefficient (β0) is calculated as (-0.0178 - 0) / 0.0139, which equals -1.28. Comparing this to the critical value of 1.96, the intercept coefficient is not statistically significant at the 5% level of significance. This means that the intercept term does not significantly differ from zero and does not contribute to the predictive power of the model. Therefore, the correct conclusion is that the slope coefficient is statistically significant, but the intercept coefficient is not, which corresponds to option D. Options A, B, and C are incorrect because they do not accurately reflect the statistical significance of the coefficients as determined by the t-test results.
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A market risk manager is assessing the performance of VTFX, a large-cap growth mutual fund. This fund is benchmarked against the MSCI World Large Cap Growth Index (MWG). To analyze the relationship, the manager performs a regression analysis using VTFX's monthly returns as the dependent variable and MWG's monthly returns as the independent (explanatory) variable. The details of the regression model and the outcomes are summarized in the table below:
| Coefficient | Estimate | Standard Error |
|---|---|---|
| β0 (Intercept) | -0.0178 | 0.0139 |
| β1 (Slope) | 1.2631 | 0.0428 |
The results of the variation analysis are provided below:
| Source of Variation | Sum of Squares | Explained | Residual |
|---|---|---|---|
| Total | 0.0527 | 0.0091 |
Given a 95% confidence level, which of the following statements would be correct for the manager to conclude?
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.