Data from portable emissions measurement systems (PEMS) and other sources have allowed the discrepancy between type approval and real-world fuel economy and nitrogen oxides (NOx) emissions to be both identified and quantified. However, a gap in the knowledge persists because identifying this discrepancy does not allow us to predict real-world fuel economy and emissions accurately. We address this gap in the knowledge using a bottom-up approach: a PEMS is used across a range of Euro 6 petrol and diesel vehicles, from which internally-consistent powertrain models are derived. These training vehicles are simulated over 20 real-world and regulated driving cycles. 26 metrics representing driving, vehicle and ambient characteristics are used to develop quantile regression (QR) models for three vehicle groups: direct-injection petrol vehicles with three way catalysts; diesel vehicles with selective catalytic reduction; and diesel vehicles with lean NOx traps. 95% prediction intervals are used to assess the predictive accuracy of the QR models from a set of validation vehicles. Across the vehicle groups, QR models for both fuel economy and NOx emissions depended on the dynamics of the driving cycles more than the engine characteristics or ambient conditions. The 95% prediction interval for fuel economy enclosed most of the observed values from the PEMS test, with similar prediction error to COPERT in most cases. The bene ts of the QR approach were more pronounced for NOx emissions, where the majority of PEMS observed data was enclosed in the 95% PI and median prediction error was up to two times lower than COPERT.