Using all variables in our data set, factor analysis led us to believe we should use ten factors. However, we did not think there should be this many factors, since we only had four principal components for our PCA. We concluded the binary variables could be causing this discrepancy. So we took the binary variables out (Sports, SUV, Wagon, Minivan, AWD, RWD) and reran our factor analysis. This time six factors was sufficient. We got a non-significant p-value for the Chi-Square test, and the smallest AIC value. We also looked at the residual correlation matrix and found the differences between the sample correlations and the new ones produced by our six-factor solution are all close to zero. Therefore, after looking at the initial factor loadings, we decided to use six factors. Looking at the factor loadings after the varimax rotation, we questioned whether factors 5 and 6 might be trivial. Even though it appeared these factors should not be used, further investigation showed us that we need to keep Weight and Width in the analysis and use six factors.

Final Factor Analysis Model
(Obtained through a Varimax Rotation)

Factor 1: This factor appears to be a measure of the size of the vehicle. The primary variables are Weight, Wheelbase, Length and Width.  Factor 2: This factor appears to be a measure of the price/cost of the vehicle. The primary variables are SRP, Dealer Cost and HP. We found the correlation between HP and SRP to be 0.835 and the correlation between HP and Dealer Cost to be 0.833. This makes sense that these variables would be highly correlated because vehicles with higher HP, such as Sports cars, tend to be more expensive. Factor 3: This factor appears to be a measure of gas mileage of the vehicle. The primary variables are Cmpg and Hwympg.  Factor 4: This factor appears to be a measure the �stuff under the hood� for a vehicle. The primary variables are Engine and Cylinders. Factor 5: This factor appears to be a measure of the weight of a vehicle.  Factor 6: This factor appears to be a measure of vehicle width.

Scatterplot Matrix

From this we can see that our factors do not seem to be correlated with one another.

Star Plot

 

The vehicles with the high factor 3 and factor 5 scores are the Hybrids (Honda Civic Hybrid, Honda Insight, and Toyota Prius). The Chevy Corvette, Chevy Corvette Convertible, Chrysler Crossfire, Ford Mustang, Ford Mustang GT Convertible, and Ford Thunderbird Deluxe have high factor 4 scores. The Hummer H2 has a large factor 5 score. The vehicles with high factor 6 scores are the Porsche 911 Carrera Convertible, Porsche 911 Carrera 4S Coupe, Porsche 911 Targa Coupe, and the lovely Porsche 911 GT2. The Porsche 911 GT2 also has a large factor 2 score because of its high price.

 

Parallel Coordinate Plot

We conditioned the colors on vehicle type. It appears from this parallel coordinate plot that the minivans have low factor 2 scores, which measures price. We can also see that the Porsche 911 GT2 has the largest factor 2. The vehicles with the largest factor 3 scores are the hybrids. Factor 3 is a measure of gas mileage, and these vehicles get the best mileage in our data. It appears the minivans and some of the SUVs have large Factor 1 score which is a measure of the overall size of the vehicle. The Sports cars tend to have large factor 6 scores which is a measure of Width.

 

 

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