A taxi company is interested in the relationship between mileage, measured inmiles per gallon, and the age of cars in its fleet.The 12 fleet cars are the same makeand size and are in good operating condition as a result of regular maintenance.The company employs both male and female drivers, and it is believed that someof the variability in mileage may be due to differences in driving techniquesbetween the groups of drivers of opposite gender. In fact, other things being equal,women tend to get better mileage than men. Data are generated by randomlyassigning the 12 cars to five female and seven male drivers and computing milesper gallon after 300 miles. The data appear in Table P-11.

a. Construct a scatter diagram with Y as the vertical axis and as the horizontalaxis. Identify the points corresponding to male and female drivers, respectively.

b. Fit the regression modeland interpret the least squares coefficient, Y = b0 + b1 X1 + b2 X2 +e

c. Compute the fitted values for each of the pairs, and plot the fitted values on the scatter diagram. Draw straight lines through the fitted values formale drivers and female drivers, respectively. Specify the equations for thesetwo straight lines.

d. Suppose gender is ignored. Fit the simple linear regression model,, and plot the fitted straight line on the scatter diagram. Isit important to include the effects of gender in this case? Explain.

Miles per gallon (Y) Age of car (years) X1 Gender (0=Male, 1=Female) X2

22.3 3 0

22.0 4 1

23.7 3 1

24.2 2 0

25.5 1 1

21.1 5 0

20.6 4 0

24.0 1 0

26.0 1 1

23.1 2 0

24.8 2 1

20.2 5 0