For the multiple regression equation developed to predict fuel efficiency (in mpg\text{mpg}) of cars based on their engine size (in L\text{L}), vehicle weight (in kg\text{kg}), and horsepower, the linear correlation coefficient (rr) was found to be r=−0.803r=-0.803.(i) What is the value of the coefficient of determination $$(R2R^2$$)?(ii) What practical information does the coefficient of determination give in this context?

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Problem 110Multiple Choice

For the multiple regression equation developed to predict fuel efficiency (in $mpg$ ) of cars based on their engine size (in $L$ ), vehicle weight (in $kg$ ), and horsepower, the linear correlation coefficient ( $r$ ) was found to be $r = - 0.803$ .
(i) What is the value of the coefficient of determination ( $R^{2}$ )?
(ii) What practical information does the coefficient of determination give in this context?

(i) $R squared equals 0.803$

(ii) The correlation between engine size and fuel efficiency is $64.5 percent sign$

(i) $R squared equals 0.645$

(ii) $64.5 percent sign$ of the variation in fuel efficiency can be explained by engine size, vehicle weight, and horsepower

(i) $R squared equals 0.645$

(ii) Increasing engine size, vehicle weight, and horsepower causes a $64.5 percent sign$ reduction in fuel efficiency

(i) $R squared equals 0.803$

(ii) The model predicts fuel efficiency with $64.5 percent sign$ accuracy

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