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=−0.985. The​ least-squares regression line treating weight as the explanatory variable and miles per gallon as the response variable is y=-0.0072 x + 45.2461.

Complete parts ​(a) through​ (c) below.

Date Set:

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 27
6 3,730 18
7 2,605 26
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

The statistical software output for this problem is:

From above output:

Proportion of variability explained

= R - square

= 97.0 %