Exploring Transmission Impact on Automobile Efficiency

Using Shiny App and MTCARS Dataset

Logan J Travis

Executive Summary

  • Many struggle to understand the impact of discrete variables in statistical models
  • Investigate automobile efficiency as a familiar and accessible example
  • Design a simple application targeting non-statisticians to:
    • Interactively model fuel efficiency (MPG) using a variety of continuous variables
      (e.g. weight, engine displacement)
    • Compare model fit after adding a discrete variable (transmission type)
  • Host the application online for all to experience!

Dataset and Methodology

MTCARS Dataset

  • Part of the base R package
  • Extracted from the 1974 Motor Trend US magazine
  • Compares fuel consumption against 10 variable for 32 automobiles

Linear Regression Models

  • Regression by transmission type yields useful results (details on next slide)
  • Attempt to improve by regressing other variables
  • Compare single variable versus adding transmission type

Example Regression Against Transmission Type

plot of chunk plotMPG~Trans

  • Linear regression for MPG ~ transmission suggests a benefit for manuals
    • The P-value for the slope (two-sided) bests a 99.9% confidence interval
    • The P-value for the intercept greatly exceeds 99.9% confidence
  • Yet, predictions from transmission alone spread +/- 10 MPG
  • Would you buy a car offering 6 to 27 MPG?
##   Transmission   Fit  Lower Upper
## 1       Manual 24.39 14.003 34.78
## 2    Automatic 17.15  6.876 27.42

Shiny App

  • Available on the Rstudio Shiny App Server

  • Input controls for predictor, interval, and color coding by transmission

  • Plots comparing single and multi-variable regression

  • Tabs for summary statistics and table data

Interpreting Results

  • Many variables yield tighter fits than transmission type notably:
    • Displacement (cu. in.) with P-value of 9.38e-10
    • Weight (lb/1000) with a P-value of 1.29e-10
  • Adding transmission type did not improve better-fit variables
  • Adding transmission type did improve predictor P-values for poorer-fit
    variables such as Gross Horsepower and 1/4 Mile Time
  • However, model quality (determined by adjusted R squared) always decreased