Question

4. The Toyota Camry is one of the best-selling cars in North America. The cost of a previously owned Camry depends on many factors, including the model year, mileage, and condition. To investigate the relationship between the car's mileage and the sales price for Camrys, the following data show the mileage and sale price for 19 sales (PriceHub web site, February 24, 2012) Miles (1,000s Price (S1,000s 16.2 29 36 47 63 73 87 92 101 110 28 59 68 68 13.8 11.5 12.5 12.9 11.2 13 11.8 10.8 8.3 12.5 11.1 15 12.2 13 15.6 12.7 8.3 42 65 110 Develop an estimated regression equation showing how price is related to miles driven. What is the estimated regression model? Test whether each of the regression parameters for the slope and the y-intercept is equal to zero at 0.01. How much of the variation in the sample values of price does the model estimated in part (a) explain? Suppose that you are considering purchasing a previously owned Camry that has been driven 60,000 miles. Use the estimated regression equation developed in part (a) to predict the price for this car. Is this the price you will offer the seller? Hint: To answer these questions, make sure you remove all the outliers that may be present in the data a. b. c. d.

Answer 1

Step-1

Create a box-plot of residuals and check the normality of residuals.

Miles	Price	Prediction	Residuals
22	16.2	15.18	1.02
29	16	14.77	1.23
36	13.8	14.35	-0.55
47	11.5	13.71	-2.21
63	12.5	12.77	-0.27
77	12.9	11.94	0.96
73	11.2	12.18	-0.98
87	13	11.36	1.64
92	11.8	11.06	0.74
101	10.8	10.53	0.27
110	8.3	10.00	-1.70
28	12.5	14.82	-2.32
59	11.1	13.00	-1.90
68	15	12.47	2.53
68	12.2	12.47	-0.27
91	13	11.12	1.88
42	15.6	14.00	1.60
65	12.7	12.65	0.05
110	8.3	10.00	-1.70

The boxplot of the residuals and the normality test for the residuals shows that there are no outliers.

(a)

Model

(b)

The respective P values of Slope of Miles and the Intercept are less than 0.01. So, the null hypothesis that their values are zero is rejected.

(c)

The R² value is 0.539 which means that 53.9% of the variation of the Price is explained by the Miles data.

(d)

Miles = 60 ('000)

So, Price (in $1,000) = -0.0588 * 60 + 16.4698 = 12.9418 i.e. $12941.8