Answer-first summary for fast verification
Answer: I and II only
## Explanation **Correct Answer: B (I and II only)** Let's analyze each statement: **I. The correlation coefficient between the X and Y variables is 0.889. ✓ CORRECT** - R² = Explained SS / Total SS = 92.648 / 117.160 = 0.791 - Correlation coefficient r = √R² = √0.791 = 0.889 **II. The industry index coefficient is significant at the 99% confidence interval. ✓ CORRECT** - t-statistic = Coefficient / Standard Error = 1.9 / 0.31 = 6.13 - With 3 degrees of freedom, critical t-value for 99% confidence is approximately 4.54 - Since 6.13 > 4.54, the coefficient is significant at 99% confidence **III. If the return on the industry index is 4%, the stock's expected return is 10.3%. ✗ INCORRECT** - Expected return = Intercept + (Coefficient × Industry return) = 2.1 + (1.9 × 4) = 2.1 + 7.6 = 9.7% - Not 10.3% **IV. The variability of industry returns explains 21% of the variation of company returns. ✗ INCORRECT** - R² = 0.791, meaning 79.1% of variation is explained, not 21% Therefore, only statements I and II are correct.
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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
