An engineer collects the following data showing the speed and miles per gallon of a Toyota Camry.

(a) Draw a scatter diagram of the data. What type of relation appears to exist between x and y?
(b) Find the quadratic regression equation y̅ = b0 + b1x + b2x2.
(c) Draw a residual plot against the fitted values, x, and x2. Also, draw a boxplot of the residuals. Are there any problems with the model?
(d) Interpret the coefficient of determination.
(e) Does the F-test indicate that we should reject H0: b1 = b2 = 0? Is either coefficient not significantly different from zero?
(f) Construct and interpret 95% confidence and prediction intervals for miles per gallon at a speed of 48 miles per hour.