A firm bids on used cars sold at auctions in the US. Most of the cars in these auctions are American made, but a few are not. The data in this analysis are a sample of 1,873 recent cars sold at auction. Most of the variables are self-­‐explanatory. The objective is to build a statistical model that predicts the cost at which a car will be sold in the auction. This would be used to help the firm’s bidder participate in the auction more competitively. The variables are listed below, and histograms/bar charts for these variables follow on the next page. Refer to the descriptive statistics on the next page for the number of categories of indicated categorical variables. The summary of a multiple regression follows the descriptive statistics. I suggest you begin by taking a few minutes to look over the fitted model and get a sense for what it does before diving into the questions. Not all of the enormous JMP output for this regression is shown, but you have what is needed for the questions. Variable Name Vehicle Cost Purchase Date Auction Average Price Auction Clean Price Current Auction Average Price Vehicle Odometer Vehicle Age Main Colors Transmission Top 3 American Brand Vehicle Type Vehicle Size Is Online Sale Warranty cost Description Response, in dollars From Nov 2008 through Feb 2011 For this type of vehicle As above, but in very good condition Recent update of the price Miles on the vehicle In years Most common 9 colors and “other” Automatic or manual GM, Ford, Chrysler, and Other SUV, car, truck, other Small, medium, large, other Whether purchase was made via Internet [0=no] To extend warranty on this vehicle Regression Model Summary of Fit
RSquare
RSquare Adj
Root Mean Square Error
Mean of Response
Observations (or Sum Wgts)
Analysis of Variance
Source
DF
Model
46
Error
1826
C. Total
1872
0.767895
0.761917
835.3222
6709.395
1873
Sum of Squares
4212966559
1273417828
5486384387
Effect Tests
Source
Purchase Date
Auction Average Price
Auction Clean Price
Current Auction Average Price
VehOdo
Vehicle Age
Main Colors
Transmission
Top Three American Brand
Vehicle Type
Vehicle Size
Vehicle Size*Top Three American Brand
Vehicle Type*Top Three American Brand
IsOnlineSale
WarrantyCost
IsOnlineSale*WarrantyCost
Mean Square
89637586
697763.19
DF
1
1
1
1
1
1
9
1
3
4
2
6
12
1
1
1
F Ratio
128.4642
Prob > F
<.0001*
Sum of Squares
71281076
39707355
15966020
33435262
61669893
31454729
8776522
31380873
13807829
194253343
82906457
19836970
34390083
3894829
12107705
3650721
F Ratio
102.1565
56.9066
22.8817
47.9178
88.3823
45.0794
1.3976
44.9735
6.5962
69.5986
59.4087
4.7382
4.1072
5.5819
17.3522
5.2320
Prob > F
<.0001*
<.0001*
<.0001*
<.0001*
<.0001*
<.0001*
0.1836
<.0001*
0.0002*
<.0001*
<.0001*
<.0001*
<.0001*
0.0183*
<.0001*
0.0223*
I abbreviated some of the names of some of the variables to be able to fit the output on a page. Further diagnostic plots follow. Parameter Estimates
Term
Intercept
Purchase Date
Auction Average Price
Auction Clean Price
Current Auction Average Price
Vehicle Odometer
Vehicle Age
Main Colors[BLACK]
Main Colors[BLUE]
Main Colors[GOLD]
Main Colors[GREEN]
Main Colors[GREY]
Main Colors[MAROON]
Main Colors[OTHER]
Main Colors[RED]
Main Colors[SILVER]
Transmission[AUTO]
Top 3 Amer Brand[CHRYSLER]
Top 3 Amer Brand[FORD]
Top 3 Amer Brand[GM]
Vehicle Type[Car]
Vehicle Type[Other]
Vehicle Type[SUV]
Vehicle Type[Truck]
Vehicle Size[Large]
Vehicle Size[Medium]
Vehicle Size[Large]*Top 3 Amer Brand[CHRYSLER]
Vehicle Size[Large]*Top 3 Amer Brand[FORD]
Vehicle Size[Large]*Top 3 Amer Brand[GM]
Vehicle Size[Medium]*Top 3 Amer Bra.[CHRYSLER]
Vehicle Size[Medium]*Top 3 Amer Bra.[FORD]
Vehicle Size[Medium]*Top 3 Amer Bra.[GM]
Vehicle Type[Car]*Top 3 Amer Bra.[CHRYSLER]
Vehicle Type[Car]*Top 3 Amer Bra.[FORD]
Vehicle Type[Car]*Top 3 Amer Bra.[GM]
Vehicle Type[Other]*Top 3 Amer Bra.[CHRYSLER]
Vehicle Type[Other]*Top 3 Amer Bra.[FORD]
Vehicle Type[Other]*Top 3 Amer Bra.[GM]
Vehicle Type[SUV]*Top 3 Amer Bra.[CHRYSLER]
Vehicle Type[SUV]*Top 3 Amer Bra.[FORD]
Vehicle Type[SUV]*Top 3 Amer Bra.[GM]
Vehicle Type[Truck]*Top 3 Amer Bra.[CHRYSLER]
Vehicle Type[Truck]*Top 3 Amer Bra.[FORD]
Vehicle Type[Truck]*Top 3 Amer Bra.[GM]
IsOnlineSale[0]
WarrantyCost
IsOnlineSale[0]*(WarrantyCost-1296)
Estimate
-33110.02
1.1327e-5
0.613995
-0.253226
0.1683536
-0.01549
129.09454
62.009806
-0.474759
-104.0886
-127.4104
141.37979
61.554401
-57.42243
16.969579
44.9186
360.03817
99.643386
-217.087
147.70561
-370.7403
536.33321
645.5742
237.17621
807.77806
-177.488
-129.5469
174.9798
364.37519
218.15457
-333.6154
-140.5801
-307.1397
226.5815
51.337799
-155.451
215.85179
-171.2013
-1.286349
290.61575
126.15277
497.51201
-141.6751
-233.7391
-60.40332
-0.454178
0.2296628
Std Error
3719.755
1.121e-6
0.073469
0.05995
0.024321
0.001648
19.22733
63.20347
52.85879
72.57386
84.00387
57.20624
99.39944
90.34509
63.21847
44.48739
53.68711
58.91699
62.05953
62.62774
72.51502
105.3914
74.98925
101.1076
98.48912
59.94318
179.0836
138.0891
146.6206
112.6318
93.03147
86.88937
121.8056
106.6716
105.274
165.0652
158.7089
132.4042
122.8566
108.5935
102.3767
172.2235
142.3914
156.6024
59.10591
0.109031
0.100405
t Ratio
-8.90
10.11
8.36
-4.22
6.92
-9.40
6.71
0.98
-0.01
-1.43
-1.52
2.47
0.62
-0.64
0.27
1.01
6.71
1.69
-3.50
2.36
-5.11
5.09
8.61
2.35
8.20
-2.96
-0.72
1.27
2.49
1.94
-3.59
-1.62
-2.52
2.12
0.49
-0.94
1.36
-1.29
-0.01
2.68
1.23
2.89
-0.99
-1.49
-1.02
-4.17
2.29
Prob>|t|
<.0001*
<.0001*
<.0001*
<.0001*
<.0001*
<.0001*
<.0001*
0.3267
0.9928
0.1517
0.1295
0.0135*
0.5358
0.5251
0.7884
0.3128
<.0001*
0.0910
0.0005*
0.0185*
<.0001*
<.0001*
<.0001*
0.0191*
<.0001*
0.0031*
0.4695
0.2053
0.0130*
0.0529
0.0003*
0.1059
0.0118*
0.0338*
0.6258
0.3464
0.1740
0.1962
0.9916
0.0075*
0.2180
0.0039*
0.3199
0.1357
0.3069
<.0001*
0.0223*
VIF
.
1.1
84.8
69.6
9.1
1.6
3.1
2.8
2.3
3.2
3.9
2.5
4.9
4.3
2.7
2.0
1.1
4.3
3.3
5.0
5.7
6.8
3.4
3.8
7.5
5.2
10.1
5.8
7.1
13.9
6.5
9.0
14.7
6.7
8.6
4.5
2.2
6.6
4.5
2.0
3.0
5.3
2.1
3.2
1.1
13.3
11.3
Diagnostic Model