Cars depreciate over time, whether made by Honda or, in this case, Toyota. These data show the prices of Toyota Camrys listed for sale by individuals in The Philadelphia Inquirer. One column gives the asking price (in thousands of dollars) and a second column gives the age (in years).
(a) Do you expect the resale value of a car to drop by a fixed amount each year?
(b) Fit a linear equation with price as the response and age as the explanatory variable. What do the slope and intercept tell you, if you accept this equation’s description of the pattern in the data?
(c) Plot the residuals from the linear equation on age. Do the residuals suggest a problem with the linear equation?
(d) Fit the equation
Estimated Price = b0 + b1 log (Age)
Do the residuals from this ft “fix” the problem found in part (c)?
(e) Compare the fitted values from this equation with those from the linear model. Show both in the same scatterplot. In particular, compare what this graph has to say about the effects of increasing age on resale value.
(f) Compare the values of r2 and se between these two equations. Give units where appropriate. Does this comparison agree with your impression of the better model? Should these summary statistics be compared?
(g) Interpret the intercept and slope in this equation.
(h) Compare the difference in asking price for cars that are 1 and 2 years old to that for cars that are 11 and 12 years old. Use the equation with the log of age as the explanatory variable. Is the difference the same or different?