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)

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Explanation:

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._

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Statistical Significance Test for DB Coefficient

Test Statistic Calculation

Critical Value

Decision

Conclusion

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