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Answer: The ratio of the variation explained by the regression to the total variation in the data about its mean is 0.831.
## Explanation **A is correct** because R² (coefficient of determination) measures the proportion of the total variation in the dependent variable that is explained by the independent variable(s) in the regression model. An R² of 0.831 means that 83.1% of the variation in the stock returns can be explained by the variation in the market index returns. **B is incorrect** because R² is not a weighted covariance measure. R² is actually the square of the correlation coefficient (r), not a covariance measure. **C is incorrect** because R² measures how much of the variation in the dependent variable (stock returns) is explained by the independent variable (market returns), not the relationship between the independent variable and model errors. A high R² indicates that most variation in the dependent variable is correlated with the independent variable, not with the errors. **D is incorrect** because R² does not measure the slope or the magnitude of the relationship between variables. The interpretation of "stock return increases by 0.831% when market index increases by 1%" would correspond to the regression coefficient (beta), not R². R² measures the goodness of fit, not the slope of the relationship.
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A junior analyst at a wealth management firm is performing a regression analysis that uses the return of a stock as the dependent variable and the market index return as the independent variable. From the results of the regression, the analyst calculates the R² measure of fit as 0.831. Which of the following statements would the analyst be correct to conclude from the calculated R² value?
A
The ratio of the variation explained by the regression to the total variation in the data about its mean is 0.831.
B
The weighted covariance between the stock return and the market return is 0.831.
C
An R² of 0.831 implies that most of the variation in the independent variable is correlated with the variation in the model errors.
D
An R² of 0.831 implies that the stock return increases by an average of 0.831% when the market index return increases by 1%.
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