The accompanying data represent the weights of various domestic cars and their g

Question

The accompanying data represent the weights of various domestic cars and their gas mileages in the city. The linear correlation coefficient between the weight of a car and its miles per gallon in the city is r=-0.987. The least squares regression line treating weight as the explanatory variable and miles per gallon as the response variable is y =-0.0073x + 45.1586. Complete parts (a) through (c) below Click the icon to view the data table (a) What proportion of the variability in miles per gallon is explained by the relation between weight of the car and miles per gallon? The proportion of the variability in miles per gallon explained by the relation between weight of the car and miles per gallon is 1 % (Round to one decimal place as needed.) (b) Construct a residual plot to verify the requirements of the least-squares regression model. Choose the correct graph below OA. oc. Residual Residual Residual Residual 2500 3250 4000 Weight (pounds) 2500 3250 4000 Weight (pounds) 2500 3250 4000 Weight (pounds) 2500 3250 4000 Weight (pounds) (c) Interpret the coefficient of determination and comment on the adequacy of the linear model % of the variance in Tis plot (Round to one decimal place as needed.) | | by the linear model. The least-squares regression model appears to be |, based on the residual

Explanation / Answer

The regression equation is

y=45.456- 0.0073(x)

a) The proportion of the variability in miles per gallon is explained by the relation between weight of the car and miles per galon is r2= (-0.987)2 =0.974

b) The regression graph:

Option C is correct.

c)hence 97% of the variance in y is explained by the linear model

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