Eigenvalues


Eigenvalues of the Correlation Matrix

Eigenvalue

Difference

Proportion

Cumulative

1

7.39955623

4.56261717

0.4353

0.4353

2

2.83693906

1.08161046

0.1669

0.6021

3

1.75532860

0.68218554

0.1033

0.7054

4

1.07314306

0.12899686

0.0631

0.7685

5

0.94414620

0.19400994

0.0555

0.8241

6

0.75013626

0.25703894

0.0441

0.8682

7

0.49309732

0.02101402

0.0290

0.8972

8

0.47208330

0.04784352

0.0278

0.9250

9

0.42423977

0.11504363

0.0250

0.9499

10

0.30919614

0.15578419

0.0182

0.9681

11

0.15341195

0.02481407

0.0090

0.9771

12

0.12859787

0.03195290

0.0076

0.9847

13

0.09664498

0.02484227

0.0057

0.9904

14

0.07180271

0.01335131

0.0042

0.9946

15

0.05845140

0.02599332

0.0034

0.9980

16

0.03245808

0.03169101

0.0019

1.0000

17

0.00076708

0.0000

1.0000



Scree Plot











According to the eigenvalues, it appears four or five principal components should be used for the analysis.  The first four eigenvalues were all greater than one.  The fifth eigenvalue was close to one, but it does not explain more of the variability than any one individual variable would (1/17 � 0.0588).  76.85% of the variability is explained by the first four principal components, and 82.41% of the variability is explained by the first five principal components.  The scree plots also suggest we should use the first four principal components.  The plot starts to slightly level off at the fifth principal component.



Principal Components

Prin1

Prin2

Prin3

Prin4

Sports

0.034248

0.442066

-.089001

-.271723

SUV

0.129805

-.224212

-.493642

-.152413

Wagon

-.031771

-.019550

-.028867

0.862708

Minivan

0.053535

-.207014

0.276028

-.341532

AWD

0.092776

-.143740

-.551073

0.080692

RWD

0.117336

0.374878

0.243227

0.075547

SRP

0.258893

0.345468

-.016672

0.046504

DealerCost

0.257356

0.346102

-.014498

0.051591

Engine

0.339550

0.002649

0.048765

-.001305

Cylinders

0.326164

0.079670

0.065943

0.056018

Hp

0.311395

0.234928

-.004498

0.018717

Cmpg

-.306206

0.017018

0.141743

0.004267

Hwympg

-.306161

0.043666

0.247651

0.026109

Weight

0.331723

-.182569

-.085671

0.014675

WheelBase

0.254688

-.306301

0.284592

0.057582

Length

0.240991

-.269975

0.335648

0.099536

Width

0.288698

-.216703

0.137418

-.085770


When looking at the first four principal components, we noticed some interesting patterns.

Principal Component #1:  This principal component appears to be a contrast between Cmpg, and Hwympg versus SUV, AWD, RWD, SRP, DealerCost, Engine, Cylinders, Hp, Weight, WheelBase, Length, and Width.  It almost seems to be comparing vehicles with high and low gas mileages.  For instance, vehicles that get lower gas mileages tend to have larger engines, more horsepower and cylinders, and bigger weights and sizes.  Therefore, this principal component might be suggesting that vehicles with higher city and highway gas mileages will have lower principal component 1 scores, whereas vehicles with lower city and highway gas mileages may have higher principal component 1 scores.


Principal Component #2:  This principal component appears to be a contrast between Sports, RWD, SRP, DealerCost, Cylinders, and Hp versus SUV, Minivan, AWD, Weight, WheelBase, Length, and Width.  Overall, it seems to be a contrast between Sports cars and other vehicles.  This is because sports cars tend to have higher SRPs and Dealer costs, more Horsepower, and are RWD, which all cause the principal component 2 scores to increase.

Principal Component #3: This principal component appears to be a contrast between Sports, SUV, AWD, and Weight versus Minivan, RWD, Cylinders, Cmpg, Hwympg, WheelBase, Length, and Width.  This could possibly be interpreted as a contrast between minivans and SUVs.

Principal Component #4: This principal component appears to be a contrast between Sports, SUV, Minivan, and Width versus Wagon, AWD, RWD, and Length. A more simple explanation of the contrast in this case could be that it is a contrast between Wagon and the other vehicle types.

Let's check out some plots to help visualize these patterns....

Plots

                                                Red = Sports Cars        Blue = Other Vehicles
 
 
 
                                                Red = Cars        Blue = Other Vehicles
 
 
 
                                                Red = SUVs        Blue = Other Vehicles
 
 
 
                                                Red = Wagons        Blue = Other Vehicles
 
 
 
                                                Red = Minivans       Blue = Other Vehicles
 
 
 
                Red = Cmpg >=19 (median)        Blue = Cmpg < 19 (median)
 
 
 





















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