Financial Risk Manager Part 1

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Explanation:

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.

Explanation:

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.

Comments (1)

Nicholas MuuzoleehJun 19, 2026 9:44 AM

these figures do not match what we have in the question

LeetQuiz .Jun 19, 2026 10:31 AM

Hi Nicholas, thank you for pointing that out. We’ve revised the figures, and the correct answer remains B because the computed R² = 0.791 gives r = 0.889, and the t‑statistic (6.13) exceeds the 99 % critical value. Thanks for your feedback.

Comments (1)

Nicholas MuuzoleehJun 19, 2026 9:44 AM

these figures do not match what we have in the question

LeetQuiz .Jun 19, 2026 10:31 AM

A regression of a stock's return (in percent) on an industry index's return (in percent) provides the following results:

Variable Coefficient Standard Error
Intercept 2.1 2.01
Industry Index 1.9 0.31

Source Degrees of Freedom Sum of Squares
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.

Variable	Coefficient	Standard Error
Intercept	2.1	2.01
Industry Index	1.9	0.31

Source	Degrees of Freedom	Sum of Squares
Explained	1	92.648
Residual	3	24.512
Total	4	117.160

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Last updated: June 19, 2026 at 10:29

III only

33.3%

I and II only

26.7%

II and IV only

20.0%

I, II, and IV

20.0%