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Answer: The correlation between the return on the stock and the return on the market is -0.90.
**Explanation:** 1. **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 2. **$R^2$ Interpretation:** $R^2 = 81\%$ means that approximately 81% of the variation in R is explained by MR. 3. **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: $r = \text{sign}(b) \times \sqrt{R^2}$.
Author: Nikitesh Somanthe
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The return on a stock (R) exhibits the following relationship with the market return (MR).
Assuming all coefficients are significant, which of the following interpretations is correct?
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.
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