Analysis of new car data

1
Analysis of new car data

• Roy Clemons
• Emily Hollister
• Stat 653
• November 2004

2
Data Set

• 2004 New Car and Truck data
• Obtained from www.amstat.org
• Based on Kiplingers Personal Finance report,
  December 2003

3
Design

• Experimental unit Vehicle Type
• Number of populations 271
• Analyzed a subset of vehicles based on a price
  range 30,000 - 40, 000
• Variables used
• Dependent City Mileage (mpg)
• Independent Horsepower, Vehicle Weight (lbs),
  and Engine Size (liters)
• Factors Vehicle type (Sedan vs. SUV)

4
Working Model

• Ymileage µi ß1ixhorse ß2ixwt ß3ixeng
• Unknown parameters
• Intercepts for Sedan and SUV
• Slopes of Vehicle weight, Horsepower, and Engine
  size as related to city mileage

5
Hypotheses
Sedan 1 SUV 2

• H0 µ1 µ2
• H0 ß11 ß12 (Slope of XHorsepower)
• H0 ß21 ß22 (Slope of XWeight)
• H0 ß31 ß32 (Slope of XEngine Size)

6
Analysis

• Removed outliers based on St. Deviation
• Hybrid and diesel-powered vehicles
• Honda Insight, Toyota Prius, Honda Civic Hybrid,
  and Volkswagen Jetta GLS TDI
• Other mileage outliers
• Land Rover Disco, Hummer H2, and Audi S4 Quattro

N 258 with outliers removed
7
Analysis continued

• 2. Set up model in GLM to test normality of
  residuals.
• 3. Saved design matrix, checked for
  multicollinearity, and used the BP test to check
  equality of variance.
• Residuals were not normal
• Variance was not equal between vehicle types
• Collinearity diagnostics were high (multiple
  values gt10.)

8
Transformation and Standardization

• Box-Cox indicated y-1 produced the most
  appropriate fit for our data
• The independent variables were standardized

9
Analysis

• Transformations corrected issues of normality,
  equality of variance.

Tests of Normality
Breusch-Pagan test for Heteroscedasticity
(CHI-SQUARE dfP) 8.846 Significance level of
Chi-square dfP (H0homoscedasticity) .3554
10
and multicollinearity!
Coefficients(a)
a Dependent Variable inv_cmpg
11
Model Fit
12
Testing Hypotheses

• Used GLM L-matrix to test our hypotheses
  concerning intercepts and slopes
• Significant differences were found (p0.05) for
• Intercepts
• Slopes of Xhorse, Xeng
• No significant difference was found between the
  slopes of Xwt
• Significance value 0.149

13
Subset Selection

• Horsepower appeared to be important in the model
  but not for both vehicle types.
• Subset selection revealed that Horsepower is an
  important factor for Sedan mileage but not for
  SUV mileage

14
Subset selection models

• Sedan
• Y-1mileage µ1 ß1xz_horse ß21xz_wt
  ß31xz_eng
• SUV
• Y-1mileage µ2 ß22xz_wt ß32xz_eng

Though the ß21 and ß22 values were not found to
be significantly different from one another (via
L-matrix test), they were still included in the
subset selection.
15
Final models

• Sedan
• Y-1mileage µ1 ß1xz_horse ß2xz_wt
  ß31xz_eng
• SUV
• Y-1mileage µ2 ß2xz_wt ß32xz_eng
• We used a common slope for X z_wt

16
Conclusions

• Estimating the city fuel economy of 2004 Sedans
  and SUVs requires 2 different models.
• Models explain 88 of the variance of city fuel
  economy
• Removal of outliers, transformation of Y, and the
  standardization of the independent variables were
  necessary to meet statistical assumptions.