Explanation:
A is correct. measures the percentage of the variation in the data that can be explained by the model. This is equivalently measured by the ratio of the explained variation to the total variation of the data (which is equal to $1 - \text{the ratio of the residual variation to the total variation}$).
B is incorrect. The measure is the squared sample correlation between the dependent and the explanatory variable.
C is incorrect. measures the percentage of the variation in the data that can be explained by the model. Since the stated is greater than 0.50, the majority of the variation in the dependent variable is correlated with the variation in the independent variable and not in the model errors.
D is incorrect. This is not the interpretation of the measure in a linear regression with a single explanatory variable. An measure of 0.831 indicates that 83.1% of the total variation in the dependent variable can be explained by the independent/explanatory variable. On the other hand, it is the beta coefficient (slope) of the regression that estimates the effect of an independent variable on the dependent variable.
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Question 47: 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 measure of fit as 0.831. Which of the following statements would the analyst be correct to conclude from the calculated 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 of 0.831 implies that most of the variation in the independent variable is correlated with the variation in the model errors.
D
An 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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