The Gas Guzzling Luxurious Cars

1. The Gas Guzzling Luxurious Cars Tony Dapontes and Danielle Sarlo

2. Our Process • From a list of sixteen luxury automobile companies, we randomly selected 10 makes using a random number generator. • Once we found these makes, we randomly selected one of their 2008 luxury models also using a random number generator, and put these models to the test!

3. Our Models Acura RL Audi S8 BMW 550 Infiniti M45 Land Rover LR3 Lexus LS460 Mercedes-Benz S550 Porsche 911 Carrera Rolls-Royce Phantom Volvo S80

4. We want to predict average MPG from the specs of the cars • What we tested… • Price • Curb Weight (lbs) • Engine Size (L) • Fuel Capacity (L) • Horsepower (HP)

5. Our first multiple regression using all 5 specs yielded high p-values for fuel capacity, price, and horsepower so we removed them from our test.

6. Assumptions/Conditions: Straight Enough Curb Weight vs. Avg MPG There appears to be random scatter in the residual plot, qualifying as Straight Enough!

7. Assumptions/Conditions: Straight Enough Engine Size vs. Avg MPG There is no pattern in the residual plot, so this condition is satisfied!

8. Assumptions/Conditions: Independence Condition One vehicle’s specs do not affect the specs of another make’s vehicle, therefore there is no reason to think there is an influence on another.

9. Assumptions/Conditions: Does the plot thicken? All of the scatter plots of the residuals are uniformly spread across the line.

10. Assumptions/Conditions: Nearly Normal We will assume that this condition is satisfied being unimodal and symmetric since this test can not be run on Fathom.

11. All of our conditions have been met so we will create a multiple regression model using Fathom…

12. ANOVA Table

13. What our results mean… (interpretation of R2 and coefficients) • Curb Weight and Engine Size account for about 88.5% of the variability in average MPG. • The regression equation indicates that each pound a car weighs is associated with about a 0.0025% decrease in average MPG. Each liter in engine size is associated with about a 0.570% decrease in average MPG.

14. The p-value for the engine size in the multiple regression is still too high, so we will remove it and find that the best predictor of average mpg is solely the curb weight of the vehicle.

15. Well… it may not be a multiple regression, but we still found a very good predictor for our luxury vehicles!

16. Our Conclusion Curb weight alone accounts for about 85.7% of the variability in average MPG. We found that the best predictor of average MPG for our luxury vehicles was just curb weight in pounds.