Explanation:
The of the regression is calculated as , which means that the variation in industry returns explains 79% of the variation in the stock return. By taking the square root of , we can calculate that the correlation coefficient () = 0.889. The -statistic for the industry return coefficient is $1.9 / 0.31 = 6.13R_{\text{stock}} = 1.9X + 2.11.9`(4%) + 2.1 = 9.7%$.
(Book 2, Module 18.2, LO 18.b)
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Question 80
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 | 2.01 |
| Industry index | 1.9 | 0.31 |
| 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 incorrect?
A
The correlation coefficient between the X and Y variables is 0.889.
B
The industry index coefficient is significant at the 99% confidence interval.
C
If the return on the industry index is 4%, the stock’s expected return is 9.7%.
D
The variability of industry returns explains 21% of the variation in company returns.
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