Explanation:
The R2 of the regression is calculated as ESS/TSS = (92.648/117.160) = 0.79, which means that the variation in industry returns explains 79% of the variation in the stock return. By taking the square root of R2, we can calculate that the correlation coefficient (r) = 0.889. The t-statistic for the industry return coefficient is 1.91/0.31 = 6.13, which is sufficiently large enough for the coefficient to be significant at the 99% confidence interval. Since we have the regression coefficient and intercept, we know that the regression equation is R stock = 1.9X + 2.1. Plugging in a value of 4% for the industry return, we get a stock return of 1.9 (4) + 2.1 = 9.7%.
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A regression of a stock’s return (in percent) on an industry index’s return (in percent) produced the following:
Coefficients
| Term | Coefficient | Standard Error |
|---|---|---|
| Intercept | 2.1 | 2.01 |
| Industry index | 1.9 | 0.31 |
ANOVA / Variation
| Source | Degrees of Freedom | SS |
|---|---|---|
| Explained | 1 | 92.648 |
| Residual | 3 | 24.512 |
| Total | 4 | 117.160 |
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