Financial Risk Manager Part 1

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Explanation:

The correlation coefficient is the square root of the coefficient of determination, otherwise known as the $R^2$ :

\text{Correlation coefficient} = -\sqrt{0.67} = -0.82

R^2 = 0.67 \text{ (given in the question)}

Testing for significance involves comparing the $t$ -statistics with a critical value of 2 for a confidence level. If the $t$ -statistic is higher than the critical value, the coefficient is significant.

\text{Intercept} = 72.24 / 18.88 = 3.82 \text{ (significant)} \\ \text{Variable } X = -27.22 / 29.85 = -0.91 \text{ (not significant)}

(Book 2, Module 19.2, LO 19.c)

Explanation:

The correlation coefficient is the square root of the coefficient of determination, otherwise known as the $R^2$ :

\text{Correlation coefficient} = -\sqrt{0.67} = -0.82

R^2 = 0.67 \text{ (given in the question)}

\text{Intercept} = 72.24 / 18.88 = 3.82 \text{ (significant)} \\ \text{Variable } X = -27.22 / 29.85 = -0.91 \text{ (not significant)}

(Book 2, Module 19.2, LO 19.c)

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Question 3

A data analyst has run a regression using one independent variable, $X$ . The sample size is 400, and the coefficient of determination is 0.67. The outputs are shown here:

Coefficients Standard Error
Intercept 72.24 18.88
Variable X -27.22 29.85

Which of the following statements is correct?

I. The correlation coefficient is $-0.82$ .
II. The $R^2$ is 0.67.
III. The intercept and variable $X$ are significant at a 95% confidence level.

	Coefficients	Standard Error
Intercept	72.24	18.88
Variable X	-27.22	29.85

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Last updated: July 3, 2026 at 10:47

I and II.

II and III.

I and III.

I, II, and III.