5.9 Does Fast Driving Waste Fuel? Exercise 4.8 (page 109) gives data on the fuel consumption y of a car at various speeds x. Fuel consumption is measured in mpg, and speed is measured in miles per hour. Software tells us that the equation of the least-squares regression line is FASTDR2 y=55.3286-0.02286x=55.3286-0.02286x Using this equation, we can add the residuals to the original data: Speed Fuel Residual 10 20 38.1 54.0 -17 -0.87 30 40 50 60 70 68.4 63.6 60.5 55.4 50.6 43.8 13.76 9.19 6.31 1.44 -3.13 -9.70 80

(a) Make a scatterplot of the observations, and draw the regression line on your plot.

(b) Would you use the regression line to predict y from x? Explain your answer.

(c) Verify the value of the first residual, for x = 10. Verify that the residuals have sum zero (up to roundoff error).

(d) Make a plot of the residuals against the values of x. Draw a horizontal line at height zero on your plot. How does the pattern of the residuals about this line compare with the pattern of the data points about the regression line in your scatterplot from part (a)?