DDPJgross: Modelling CO2 emissions from 1974-era Automobiles

J Gross
2016-04-16

Introduction

This project is designed to answer the question: What sort of fuel efficiency, and therefore CO2 emissions, could you expect if you were able to specify the gross weight, and transmission type, of an automobile manufactured using the technology available in 1974?

Although this proposition may appear moot from the perspective of 2016, the fundamental physics of transportation remain unchanged: an autombile with more mass produces more emissions.

The interactive application is availalbe here:
http://jef144.shinyapps.io/DDPJgross/

Source data for prediction model

Since the desire was to be able to predict emissions of an automobile, we reach back to a familiar dataset, the mtcars sample provided in the R distribution. This dataset was complied from 1974 issues of Motor Trend magazine.

Building on previous research many linear regression models were built using various combinations of predictors. The best model was found to be using vehicle weight, plus the choice of manual vs automatic transmissions, plus the interaction between these two terms:

fitwtAMCust<-lm(mpg ~ wt  +  factor(am) +   wt:factor(am) , data=mtcars)
summary(fitwtAMCust)


Call:
lm(formula = mpg ~ wt + factor(am) + wt:factor(am), data = mtcars)

Residuals:
    Min      1Q  Median      3Q     Max 
-3.6004 -1.5446 -0.5325  0.9012  6.0909 

Coefficients:
               Estimate Std. Error t value Pr(>|t|)    
(Intercept)     31.4161     3.0201  10.402 4.00e-11 ***
wt              -3.7859     0.7856  -4.819 4.55e-05 ***
factor(am)1     14.8784     4.2640   3.489  0.00162 ** 
wt:factor(am)1  -5.2984     1.4447  -3.667  0.00102 ** 
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 2.591 on 28 degrees of freedom
Multiple R-squared:  0.833, Adjusted R-squared:  0.8151 
F-statistic: 46.57 on 3 and 28 DF,  p-value: 5.209e-11

Analytical Approach

Although this model did not, in absolute terms, provide the closest fit, it was superior in being transparent and parsimonious: transparent, in that is obvious to subject matter experts from that period, that weight and transmission type would be deciding factors in fuel efficiency; parsimonious, in that only two predictor variables are required. As it turns out, requiring only two predictors increases the ease-of-use of the interactive model.

Technology Employed

The following steps were taken to use the model in a predictive, interactive manner

  • The model was stored as a file, fitwtAMCust.rds, to reduce overhead on the shiny web site
  • Values for Weight and Transmission Type are solicited using the ui.R web page
  • The predict() function was called with the model, weight, and transmission type as inputs
  • If the model predicts negative values the predicted MPG value is forced to zero
  • The output of predict is displayed both in as miles/gallon and CO2/km values

Summary

The interactive model seems to produce predictions that are consistent with the range of cars available in the 1974 period. The predictions are, from a contemporary perspective, shockingly bad and do not come close to standards soon to be imposed (US: 54.5 mpg by 2025; Europe 98 gm/km by 2020).

For comparison, an independent interactive estimator is from the Union of Conerned Scientists for electric cars. Unlike the analysis presented in this paper, the electric vehicle estimator below takes into account up-stream CO2 emissions, that is, carbon released as a by product of gasoline extraction and refining, on one hand, or electricy generation for electric cars.

http://www.ucsusa.org/clean-vehicles/electric-vehicles/ev-emissions-tool