Question

The accompanying 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 = −0.978. The​ least-squares regression line treating weight as the explanatory variable and miles per gallon as the response variable is ŷ=−0.0067x+43.2680.

Car   Weight (pounds), x   Miles per Gallon, y
1   3,765   18
2   3,984   17
3   3,530   21
4   3,175   23
5   2,580   26
6   3,730   18
7   2,605   25
8   3,772   17
9   3,310   21
10   2,991   24
11   2,752   25

​(a) What proportion of the variability in miles per gallon is explained by the relation between weight of the car and miles per​ gallon?

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.)

Answer 1

Answer (a)

given that

r = -0.978

we know that coefficient of determination tells us about the percent of variation in y due to x

and

coefficient of determination = r^2

= (-0.978)^2

= 0.956

converting to percent, we get

= 0.956*100

= 95.6%