The data in the table represent the weights of various domestic cars and their miles per gallon in the city for the 2008 model year. For these data, the least-squares regression line is y=−0.006x+42.541. A twelfth car weighs 3,425 pounds and gets 12 miles per gallon. (a) Compute the coefficient of determination of the expanded data set. What effect does the addition of the twelfth car to the data set have on R2? (b) Is the point corresponding to the twelfth car influential? Is it an outlier? Car Weight_(pounds),_x Miles_per_Gallon,_y 1 3767 21 2 3989 19 3 3534 20 4 3175 22 5 2581 27 6 3736 20 7 2606 26 8 3778 19 9 3313 21 10 2996 26 11 2757 27

Linear Algebra: A Modern Introduction

4th Edition

ISBN:9781285463247

Author:David Poole

Publisher:David Poole

Chapter7: Distance And Approximation

Section7.3: Least Squares Approximation

Problem 31EQ

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The data in the table represent the weights of various domestic cars and their miles per gallon in the city for the 2008 model year. For these data, the least-squares regression line is y=−0.006x+42.541. A twelfth car weighs 3,425
pounds and gets 12 miles per gallon.

(a) Compute the coefficient of determination of the expanded data set. What effect does the addition of the twelfth car to the data set have on R2?

(b) Is the point corresponding to the twelfth car influential? Is it an outlier?

Car Weight_(pounds),_x Miles_per_Gallon,_y
1 3767 21
2 3989 19
3 3534 20
4 3175 22
5 2581 27
6 3736 20
7 2606 26
8 3778 19
9 3313 21
10 2996 26
11 2757 27

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