-Used SAS programming to find the best characteristic (regressor) for mileage per gallon -Addressed multicollinearity, heteroskedasticity, and autocorrelation -Performed power transformation, ridge regression, and principle component regression to reduce multicollinearity

1. Collaborators:
James Patounas
Zhengang Xu
Ali Yeager

2. Introduction
• Approximately one half of the oil used in the U.S. is
imported
• Nearly $2 trillion was spent from 2004 to 2008 on oil
• New Corporate Average Fuel Economy (CAFE) standards
passed with goal of 35 mpg on average by 2020
• Decided to conduct a study on how we can reach this
goal

3. ID MY MPG WT DISP HP ACC
46 1978 9.8 4000 258 125 14.2
47 1978 11.8 4409 315 149 13.7
48 1978 12.2 4500 338 159 13.1
49 1979 15.3 3026 180 128 12.2
50 1979 21.7 2450 113 77 14.4
51 1979 19.0 2847 155 94 14.2
52 1979 15.4 3624 246 117 14.4
Light-Duty Automotive Technology,
Carbon Dioxide Emissions, and Fuel
Economy Trends: 1975 Through 2011

4. Limitations
Our Regressors Chosen
• Weight
• Engine displacement
• Horsepower
• Acceleration time
Other factors not considered
• Variable valve timing (5%)
• Cylinder deactivation (7.5%)
• Turbochargers and
superchargers (7.5%)
• Direct fuel injection (11-13%)

5. Initial Data
Viewed problems of possible multicollinearity and non-linear relationships

6. Multicollinearity
Variance Inflation
Factors are close to
or greater than 10
Condition Indices
greater than 15

7. Autocorrelation
Durbin-Watson statistic is very
close to 2
After “normalizing” data

8. Residual Plot

9. Power
transformation
Found best lambda
Maximized Log-
Likelihood and R-
squared
Applied the log function
to DISP and HP

10. Residual Plots
Residuals Before Transformation Residuals After Transformation

11. Multicollinearity
after
transformation
Still multicollinearity
problems, slightly
reduced

12. Ridge Regression to Reduce the
Multicollinearity

13. Ridge Regression to Reduce the
Multicollinearity

14. PCR-Principal Component Regression

15. Interpreting the Models

16. Future Work
• Expanding the study with current data
 Bootstrap Confidence Intervals
 Add Variables
 Time Series
• Conducting an experiment
 Sample Size
 Expand Predictors