The data represent the weights of various domestic cars and their gas mileages i

Question

The data represent the weights of various domestic cars and their gas mileages in the city. The linear correlation coefficient between the weight of a car and its miles per gallon in the city is r = -0.964. The least-square regression line treating weight as the explanatory variable and miles per gallon as the response variable is y = -0.0061x + 41.8342.

a) The proportion of the variability in miles per gallon explained by the relation between weight of the car and miles per gallon is ____% . (round to one decimal place as needed)

b) Interpret the coefficient of determination.

____% of the variance in gas mileage/weight is explained/not explained by the linear model.

Car Weight (pounds), Car 7 Car 8 Car 9 Car 10 Car 11 Miles per Weight (pounds), 3,765 3,984 3,530 3,175 2,580 3,730 Miles per Car Car 1 Car 2 Car 3 Car 4 Car 5 Car 6 Gallon, y 20 19 21 2,605 3,772 3,310 2,991 2,752 Gallon, y 26 18 21 24 25 27 18

Explanation / Answer

r = -0.964

So, r2 = 0.929296

So, 92.9% of variation is explained .

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92.9% of the variance in gas mileage is explained by the linear model.

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