Question

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

Answer 1

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%