Answer-first summary for fast verification
Answer: I and II only
## Explanation Let's analyze each statement: **I. The correlation coefficient between the X and Y variables is 0.889.** - R² = Explained SS / Total SS = 92.648 / 117.160 = 0.791 - Correlation coefficient r = √R² = √0.791 = 0.889 - ✓ **CORRECT** **II. The industry index coefficient is significant at the 99% confidence interval.** - t-statistic = coefficient / standard error = 1.9 / 0.31 = 6.13 - For 3 degrees of freedom (residual df), the critical t-value at 99% confidence (two-tailed) is approximately 5.841 - Since 6.13 > 5.841, the coefficient is significant at 99% confidence level - ✓ **CORRECT** **III. If the return on the industry index is 4%, the stock's expected return is 10.3%.** - Expected return = Intercept + (Industry coefficient × Index return) - Expected return = 2.1 + (1.9 × 4) = 2.1 + 7.6 = 9.7% - The statement says 10.3%, which is incorrect - ✗ **INCORRECT** **IV. The variability of industry returns explains 21% of the variation of company returns.** - R² = 0.791 = 79.1%, not 21% - ✗ **INCORRECT** **Conclusion:** Statements I and II are correct, so the correct answer is **B. I and II only**.
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A regression of a stock's return (in percent) on an industry index's return (in percent) provides the following results:
| Coefficient | Standard Error |
|---|---|
| Intercept | 2.1 |
| Industry index | 1.9 |
| Degrees of Freedom | SS |
|---|---|
| Explained | 1 |
| Residual | 3 |
| Total | 4 |
Which of the following statements regarding the regression is correct?
I. The correlation coefficient between the X and Y variables is 0.889.
II. The industry index coefficient is significant at the 99% confidence interval.
III. If the return on the industry index is 4%, the stock's expected return is 10.3%.
IV. The variability of industry returns explains 21% of the variation of company returns.
A
III only
B
I and II only
C
II and IV only
D
I, II, and IV
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