The data in the table represent the weights of various domestic cars and their m

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 + 40 503. A twelfth car weighs 3.425 pounds and gets 11 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? (b) Is the point corresponding to the twelfth car influential? Is it an outlier? Data Table EEB Click the icon to view the data table. (a) The coefficient of determination of the expanded data set is R4 Round to one decimal place as needed.) %. Weight (pounds), Miles per D Gallon, y 21 19 21 3,771 3,985 3,533 3,176 2,583 3,738 2,605 3,777 3,310 2,999 2,758 27 20 25 19 20 26 26 ar 11

Explanation / Answer

The statistical software output for this problem is:

Simple linear regression results:
Dependent Variable: Miles per gallon y
Independent Variable: Weight x
Miles per gallon y = 41.2543 - 0.0060023097 Weight x
Sample size: 12
R (correlation coefficient) = -0.6634693
R-sq = 0.44019151
Estimate of error standard deviation: 3.4361743

Parameter estimates:

Analysis of variance table for regression model:

Hence,

a) Coefficient of determination for extended data set = 44.0%

Parameter Estimate Std. Err. Alternative DF T-Stat P-value Intercept 41.2543 7.1435903 0 10 5.7750092 0.0002 Slope -0.0060023097 0.0021405102 0 10 -2.804149 0.0187

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