A taxi company is interested in the relationship between mileage, measured in miles per gallon, and the age of cars in its fleet. The 12 fleet cars are the same make and 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 some of the variability in mileage may be due to differences in driving techniques between 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 randomly assigning the 12 cars to five female and seven male drivers and computing miles per gallon after 300 miles. The data appear in Table P-11.
a. Construct a scatter diagram with Y as the vertical axis and X1 as the horizontal axis. Identify the points corresponding to male and female drivers, respectively.
b. Fit the regression model
Y = β0 + β1X1 + β2X2 + ε
and interpret the least squares coefficient, b2.
c. Compute the fitted values for each of the (X1, X2) pairs, and plot the fitted values on the scatter diagram. Draw straight lines through the fitted values for male drivers and female drivers, respectively. Specify the equations for these two straight lines.
d. Suppose gender is ignored. Fit the simple linear regression model, Y = β0 + β1X1 + ε, and plot the fitted straight line on the scatter diagram. Is it important to include the effects of gender in this case? Explain.
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