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Answer: Test statistic = 9.310; DB regression coefficient is statistically different from zero
## Statistical Significance Test for DB Coefficient We are testing the following hypothesis: $$H_0 : \beta_{DB} = 0 \quad \text{vs} \quad H_1 : \beta_{DB} \neq 0$$ ### Test Statistic Calculation $$t = \frac{\text{Coefficient}}{\text{Standard Error}} = \frac{0.27}{0.029} = 9.310$$ ### Critical Value - Significance level: 5% (α = 0.05) - Degrees of freedom: n - k - 1 = 43 - 2 - 1 = 40 - Critical t-value: $t_{0.025, 40} = 2.021$ ### Decision Since the test statistic (9.310) is greater than the critical value (2.021), we **reject the null hypothesis**. ### Conclusion The DB regression coefficient is statistically different from zero at the 5% level of significance. This means the trailing dividend payout ratio has a statistically significant relationship with future 15-year real earnings of the S&P 500.
Author: Tanishq Prabhu
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An analyst believes that future 15-year real earnings of the S&P 500 are a function of the trailing dividend payout ratio of the stocks in the index (DB) and the yield curve slope (YC). She collects data and obtains the following multiple regression results:
| Coefficient | Standard Error | |
|---|---|---|
| Intercept | –10.8% | 1.567% |
| DB | 0.27 | 0.029 |
| YC | 0.12 | 0.210 |
Test the statistical significance of the independent variable DB at the 5% level of significance, quoting the value of the test statistic and the conclusion. (Number of observations = 43)
A
Test statistic = 2.021; DB regression coefficient is statistically different from zero
B
Test statistic = 9.310; DB regression coefficient is statistically different from zero
C
Test statistic = 0.018; DB regression coefficient is not statistically different from zero
D
Test statistic = 9.310; DB regression coefficient has little effect on the returns of S&P 500