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 y=-0.006x + 43.516. A twelfth car weighs 3,425 pounds and gets 13 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 R^2? (b) Is the point corresponding to the twelfth car influential? Is it an outlier?

Car   Weight (pounds), x   Miles per Gallon, y
1 3771    21
2 3980 22
3 3527 20
4 3171 22
5 2578 28
6 3738 19
7 2600 27
8 3777 18
9 3312 20
10 2995 27
11 2756 27
      
      
      
      
      
      
      
      
      
      

Answer 1

Before 12th car R² is:

R²= 0.739 or 73.9%

After 12th car, R² is :

R²=0.516 or 51.6%

This shows that after adding the 12th variable in the dataset the explained variability in the dataset reduces. And if you notice then the standard error is also increasing, it also affecting the errors.

b)

As the data values of 12th car are under the quartile fences limit, since they are not the outliers.

Quartile fences calculated as followed:

Q.F= Lower fence= Q1-1.5(IQR)

Q.F= Upper fence= Q3+1.5(IQR)