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The return on a stock (R) exhibits the following relationship with the market return (MR).

R = -1.15 \times MR + 2\%; R^2 = 81\%

Assuming all coefficients are significant, which of the following interpretations is correct?

Other

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NNikitesh

Last updated: February 2, 2026 at 10:22

A

A 1% increase in MR results into a 1.15% increase in R.

B

A 1% increase in MR results into 2% increase in R.

C

The correlation between the return on the stock and the return on the market is 0.81.

D

The correlation between the return on the stock and the return on the market is -0.90.

Explanation:

Regression Interpretation: The regression equation is $R = -1.15 \times MR + 2\%$ . This means:
- The slope coefficient is -1.15, indicating an inverse relationship
- When MR increases by 1%, R changes by $-1.15 \times 1\% = -1.15\%$ (R decreases by 1.15%)
- The intercept of 2% represents the expected return when MR = 0
$R^2$ Interpretation: $R^2 = 81\%$ means that approximately 81% of the variation in R is explained by MR.
Correlation Calculation: The correlation coefficient (r) is calculated as: $r = [\text{Sign of estimated slope coefficient}] \sqrt{R^2}$ Since the slope coefficient is negative (-1.15), the correlation is negative: $$r = -\sqrt{0.81} = -0.9 $`$ 4`. Why other options are incorrect:
- Option A: Incorrect because the relationship is negative, not positive
- Option B: Incorrect because 2% is the intercept, not the slope
- Option C: Incorrect because correlation is negative (-0.90), not positive (0.81)

Key Concept: In linear regression, the correlation coefficient can be derived from $R^2$ and the sign of the slope coefficient: $r = \text{sign}(b) \times \sqrt{R^2}$ .

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