Explanation:
We are testing the following hypothesis:
H₀: β₁ = 0 vs. Hₐ: β₁ ≠ 0
The test statistic is 0.37 / 0.099 = 3.7373
t_{α/2, n−k−1} = t_{0.01, 1000} = 2.576
The test statistic (3.7373) is greater than the upper critical value (2.576) of the t-distribution with 1000 degrees of freedom. Therefore, we reject the null hypothesis and conclude that the DB regression coefficient is statistically different from zero at the 1% level of significance.
Section: Quantitative Analysis
Chapter: Regression with Multiple Explanatory Variables
Learning objective: Construct, apply and interpret joint hypothesis tests and confidence intervals for multiple coefficients in a regression
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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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