Using advertised prices for used Ford Escorts a linear model for the relationship between a car's age and its price is found.The regression has an $R2\mathrm { R } ^ { 2 }$ = 87.7%.Write a sentence summarizing what $R2\mathrm { R } ^ { 2 }$ says about this regression.

A) The age of the car explains 87.7% of the variation in price.
B) The price of the car explains 87.7% of the variation in age.
C) The age of the car explains 12.3% of the variation in price.
D) The age of the car explains 9.36% of the variation in price.
E) The price of the car explains 12.3% of the variation in age.

Question

Using advertised prices for used Ford Escorts a linear model for the relationship between a car's age and its price is found.The regression has an

R2\mathrm { R } ^ { 2 }

= 87.7%.Write a sentence summarizing what

R2\mathrm { R } ^ { 2 }

says about this regression.

A) The age of the car explains 87.7% of the variation in price.
B) The price of the car explains 87.7% of the variation in age.
C) The age of the car explains 12.3% of the variation in price.
D) The age of the car explains 9.36% of the variation in price.
E) The price of the car explains 12.3% of the variation in age.

Jashan Dhillon · Accepted Answer

Final Answer : A, Explanation :  The coefficient of determination (R-squared) value of 0.877 indicates that 87.7% of the variation in the price of used Ford Escorts can be explained by their age, thus option A is the correct answer. Option B is incorrect, as it states that the price of the car explains the variation in age, which is not what the regression model is examining. Options C, D, and E are also incorrect, as they suggest that the age or price explains less than 50% of the variation, which is not supported by the given R-squared value.

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