Question

The Toyota Camry is one of the best-selling cars in North America. The cost of a previously owned Camry depends upon many factors, including the model year, mileage, and condition. To investigate the relationship between the car’s mileage and the sales price for a 2007 model year Camry, the following data show the mileage and sales price for 19 sales (PriceHub website, February 24, 2012). Suppose that you are considering purchasing a previously owned 2007 Camry that has been driven 60,000 miles. What price you would offer to the seller and why?

Include discussion of the scatter diagram, regression equation, test for significant relationship, coefficient of determination, correlation coefficient, interpretation of the slope of the regression equation, 95% prediction interval and the 95% confidence interval of the mean sales price given mileage.

Miles (1000s)	Price ($1000s)
22	16.2
29	16
36	13.8
47	11.5
63	12.5
77	12.9
73	11.2
87	13
92	11.8
101	10.8
110	8.3
28	12.5
59	11.1
68	15
68	12.2
91	13
42	15.6
65	12.7
110	8.3

Answer 1

miles, X	Price, Y	XY	X²	Y²
22	16.20	356.4	484	262.44
29	16.00	464	841	256
36	13.80	496.8	1296	190.44
47	11.50	540.5	2209	132.25
63	12.50	787.5	3969	156.25
77	12.90	993.3	5929	166.41
73	11.20	817.6	5329	125.44
87	13.00	1131	7569	169
92	11.80	1085.6	8464	139.24
101	10.80	1090.8	10201	116.64
110	8.30	913	12100	68.89
28	12.50	350	784	156.25
59	11.10	654.9	3481	123.21
68	15.00	1020	4624	225
68	12.20	829.6	4624	148.84
91	13.00	1183	8281	169
42	15.60	655.2	1764	243.36
65	12.70	825.5	4225	161.29
110	8.30	913	12100	68.89

Sample size, n =	19
Ʃ x =	1268
Ʃ y =	238.4
Ʃ xy =	15107.7
Ʃ x² =	98274
Ʃ y² =	3078.84
x̅ =	66.73684211
y̅ =	12.54736842
SSxx = Ʃx² - (Ʃx)²/n =	13651.68421
SSyy = Ʃy² - (Ʃy)²/n =	87.54736842
SSxy = Ʃxy - (Ʃx)(Ʃy)/n =	-802.3631579

Scatter plot:

Slope, b = SSxy/SSxx =    -0.058773932          
y-intercept, a = y̅ -b* x̅ =    16.46975503          
              
Regression equation :               
ŷ = 16.4698 + (-0.0588) x

Coefficient of determination, r² = (SSxy)²/(SSxx*SSyy) = 0.5387

Correlation coefficient, r = SSxy/√(SSxx*SSyy) = -0.7339

Interpret slope:

A unit increase in the number of miles decreases the price of car by 0.0588 units.

Sum of Square error, SSE = SSyy -b*Ssxy =    40.38933
Standard error, se = √(SSE/(n-2)) =   1.54138

Predicted value at X =   60          
ŷ =16.4698 - 0.0588 * 60 = 12.943   
Price that would be offered to seller = 12.943 *1000 = $12943

At α = 0.05 and df = n-2 =17, critical value, t_c = T.INV.2T(0.05, 2) = 2.1098

95%   Prediction interval :                          
  
                              
95%   Confidence interval :