Question

In: Statistics and Probability

Do heavier cars really use more gasoline? suppose a car is chosen at random. Let x...

Do heavier cars really use more gasoline? suppose a car is chosen at random. Let x be the weight of the car (in hundreds of pounds) and let y be the miles per gallon (mpg). The following information is based on data taken from consumer reports (Vol. 62, No.4). What percentage of the variation in y can be explained by the corresponding variation in x and the least-squares line?

X 27 44 32 47 23 40 34 52
Y 30 19 24 13 29 17 21 14

Solutions

Expert Solution

Using Excel, (Data -> Data Analysis -> Regression), we get the following output -

The regression equation is :

Y = 43.33 - 0.6*X

Here,

coefficient of determination R2 = 0.8954 = 89.54%

So,

The percentage of the variation in y can be explained by the corresponding variation in x and the least-squares line

= 89.54%

orchestra answered 2 years ago
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