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:

Test the statistical significance of YCS at the 10% level of significance, quoting the t-statistic and the conclusion if n = 46.

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Explanation:

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.

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