Purchasing a service contract. The manager of a retail appliance store wants to model the proportion of appliance owners who decide to purchase a service contract for a specific major appliance. Since the manager believes that the proportion y decreases with age x of the appliance (in years), he will fit the first-order model
E(y) = β0 + β1x
A sample of 50 purchasers of new appliances are contacted about the possibility of purchasing a service contract. Fifty owners of 1-year-old machines and 50 owners each of 2-, 3-, and 4-yearold machines are also contacted. One year later, another survey is conducted in a similar manner. The proportion y of owners deciding to purchase the service policy is shown in the table.
(a) Fit the first-order model to the data.
(b) Calculate the residuals and construct a residual plot versus y^.
(c) What does the plot from part b suggest about the variance of y?
(d) Explain how you could stabilize the variances.
(e) Refit the model using the appropriate variance-stabilizing transformation. Plot the residuals for the transformed model and compare to the plot obtained in part b. Does the assumption of homoscedasticity appear to be satisfied?