Answer-first summary for fast verification
Answer: 0.884
## Explanation For a linear regression with one explanatory variable, the R² (coefficient of determination) is equal to the squared sample correlation between the dependent variable and the explanatory variable. **Mathematical relationship:** - R² = (Correlation)² - Therefore, Correlation = √R² **Calculation:** - Given R² = 0.781 - Correlation = √0.781 = 0.884 **Why other options are incorrect:** - **A (0.610)**: This is approximately the square of R² (0.781² ≈ 0.610), not the correlation - **B (0.754)**: This is the square root of the beta coefficient (√0.569 ≈ 0.754), not the correlation - **C (0.781)**: This is the R² value itself, not the correlation This relationship holds specifically for simple linear regression with one independent variable, where the correlation coefficient squared equals the R² value.
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A finance intern at a wealth management firm constructs a linear regression model that regresses the return of a stock on the market index return. After running the regression, the intern finds that the estimated coefficient for the market index return is 0.569 and that the resulting R² measure is 0.781. Which of the following would the intern be correct to calculate as the correlation between the return of the stock and the market index return?
A
0.610
B
0.754
C
0.781
D
0.884
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