Explanation:
To test the statistical significance of the independent variable DB, we calculate the t-statistic using the formula:
The degrees of freedom are . At a 1% level of significance for a two-tailed test with a large sample size (), the critical t-value is approximately 2.576.
Since the calculated test statistic (3.7373) is greater than the critical value (2.576), it falls in the rejection region. Therefore, we reject the null hypothesis and conclude that the DB regression coefficient is statistically different from zero.
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Q.6 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 | –15.2% | 3.589% |
| DB | 0.37 | 0.099 |
| YC | 0.18 | 0.133 |
If the number of observations is assumed to be 1003, test the statistical significance of the independent variable DB at the 1% level of significance, quoting the value of the test statistic and the conclusion. If needed, refer to the t-table by clicking the link below: t-distribution-table
A
Test statistic = 0.2676; The DB regression coefficient is statistically different from zero
B
Test statistic = 3.7373; The DB regression coefficient is statistically different from zero
C
Test statistic = 0.2676; The DB regression coefficient is not statistically different from zero
D
Test statistic = 3.7373; The DB regression coefficient is not statistically different from zero
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