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Answer: 8.333; The YCS coefficient is statistically significantly different from zero.
## Explanation To test the statistical significance of the YCS coefficient at the 10% level of significance: **Step 1: Calculate the t-statistic** The t-statistic for the YCS coefficient is calculated as: $$t = \frac{\text{Coefficient}}{\text{Standard Error}} = \frac{0.20}{0.024} = 8.333$$ **Step 2: Determine the critical t-value** - Sample size (n) = 46 - Number of independent variables (excluding intercept) = 2 (YCS and PR) - Degrees of freedom = n - k - 1 = 46 - 2 - 1 = 43 - For a two-tailed test at 10% significance level, the critical t-value is approximately 1.68 **Step 3: Compare and conclude** Since the calculated t-statistic (8.333) > critical t-value (1.68), we reject the null hypothesis that the YCS coefficient equals zero. **Conclusion**: The YCS coefficient is statistically significantly different from zero at the 10% level of significance. **Note**: The question specifically asks to test YCS, not PR. The t-statistic for PR would be 0.12/0.230 = 0.522, which is not statistically significant.
Author: Tanishq Prabhu
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A market analyst has established that future 10-year growth of earnings in the S&P 500 can be explained by a combination of two factors: the slope of the yield curve (YCS) and the preceding dividend payout ratio (PR) of stocks that have been featured in the index. The analyst carries out a regression and obtains the following results:
| Coefficient | Standard error | |
|---|---|---|
| Intercept | –10.6% | 1.525% |
| YCS | 0.20 | 0.024 |
| PR | 0.12 | 0.230 |
Test the statistical significance of YCS at the 10% level of significance, quoting the t-statistic and the conclusion if n = 46.
A
16.60; The YCS coefficient is statistically significantly different from zero.
B
16.60; The PR coefficient is statistically significantly different from zero.
C
8.333; The YCS coefficient is statistically significantly different from zero.
D
1.68; The YCS coefficient is not statistically significantly different from zero.