Question

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 ModifyingAbove y with -0.006x + 42.216. 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 Rsquared​? ​

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

Car, Weight (pounds) x, Miles per Gallon y
1 3766 20
2 3989 21
3 3532 20
4 3170 22
5 2575 28
6 3735 20
7 2605 27
8 3772 18
9 3310 19
10 2993 26
11 2755 25

Answer 1

Solution:

​(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 R-squared​? ​

Answer: We can use the excel regression data analysis tool to find the coefficient of determination. The excel output is given below:

Therefore, the coefficient of determination is 0.4929. Addition of the twelfth car has reduced the R-squared value of the model.

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

Answer: The point corresponding to the twelfth car is an outlier.