A study of new cars to predict city gas mileage (miles per galon) from their wei

Question

A study of new cars to predict city gas mileage (miles per galon) from their weight (pounds) resulted in a correlation coefficient of r= -0.4. Based on this information, which of the following statement is correct?

a. the fact that cars have different gas mileages explains about 60% of the observed variation in the car weights.

b. the fact that cars have different gas mileages explains about 80% of the observed variation in the car weights.

c. the fact that cars have different weights explains about 40% of the ovserved variation in their gas mileages.

d.  the fact that cars have different weights explains about 16% of the ovserved variation in their gas mileages.

Explanation / Answer

Coefficient of determination = r2 = (-0.4)2 = 0.16 i.e. 16%

So,

the fact that cars have different weights explains about 16% of the ovserved variation in their gas mileages.

Option D is correct.

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