Modelling Fuel Consumption of Cars by Method of Cauchit Quantile Regression (Published)
Fuel consumption is a major operational cost for vehicle owners and transport operators and is closely associated with energy efficiency and environmental sustainability. Conventional mean-based methods such as Ordinary Least Squares (OLS) regression may be inadequate for fuel consumption data characterized by skewness, heavy tails, and outliers. This study therefore applies Cauchit Quantile Regression (CQReg), a robust modelling technique that combines the distributional flexibility of quantile regression with the heavy-tailed properties of the Cauchy distribution, to model car fuel consumption. The study utilized data from 91 cars, with miles per gallon (MPG) as the response variable and car weight, length, wheelbase, width, engine size, and horsepower as explanatory variables. The CQReg model was fitted at the 0.05, 0.25, 0.50, 0.75, and 0.95 quantiles. Bootstrap resampling with 200 replications was employed to estimate standard errors, confidence intervals, and p-values. Model adequacy was assessed using pseudo-R², Akaike Information Criterion (AIC), and residual diagnostics. The results revealed that car weight and length were the most important predictors of fuel consumption across the middle quantiles. At the 0.25 and 0.50 quantiles, both weight and length had statistically significant effects, while at the 0.75 quantile, weight and length also remained significant. However, none of the predictors was statistically significant at the 0.05 and 0.95 quantiles, suggesting greater variability at the extremes of fuel consumption. The CQReg models produced relatively low AIC values and small prediction errors, indicating satisfactory model performance. The study concludes that CQReg provides a robust and informative approach for modelling fuel consumption and is recommended for analyzing vehicle fuel consumption data containing outliers and heavy-tailed characteristics.
Keywords: Bootstrap regression, Cauchit Quantile Regression, Cauchy distribution, Fuel Consumption, Fuel efficiency, Heavy-tailed data, Model selection, Outliers