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Answer: 0.952, indicating that the variability of industry sales explains about 95.2% of the variability of company sales.
## Explanation R² (coefficient of determination) is calculated as the square of the correlation coefficient (r). Given: - Correlation (r) = 0.9757 - R² = r² = (0.9757)² ≈ 0.952 **Interpretation of R²:** - R² represents the proportion of variance in the dependent variable that is explained by the independent variable - In this context, if we consider industry sales as the independent variable and company sales as the dependent variable, then R² = 0.952 means that 95.2% of the variability in company sales is explained by the variability in industry sales **Why option C is correct:** - The value 0.952 is the correct R² calculation (0.9757² ≈ 0.952) - The interpretation correctly states that industry sales (independent variable) explains company sales (dependent variable) - This makes economic sense as industry trends typically drive individual company performance **Why other options are incorrect:** - Options A and B: Use incorrect value (0.048 instead of 0.952) - Option D: Has the correct value but incorrect interpretation - it reverses the relationship between independent and dependent variables
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The correlation between company and industry sales is 0.9757. Which of the following is closest to the value and reports the most likely interpretation of the R²?
A
0.048, indicating that the variability of industry sales explains about 4.8% of the variability of company sales.
B
0.048, indicating that the variability of company sales explains about 4.8% of the variability of industry sales.
C
0.952, indicating that the variability of industry sales explains about 95.2% of the variability of company sales.
D
0.952, indicating that the variability of company sales explains about 95.2% of the variability of industry sales.