Selection of explanatory variables

The explanatory variable explains changes in the response variable; mean positive acceleration. All vehicles encounter the same obstacles. However, the variation in the response variable may be explained by the use of different vehicles, some of which may be able to accelerate more quickly than others. Emissions Analytics collect metadata for each vehicle test, however complete data was only available for the vehicle characteristics shown in Table 4.3.

Characteristic Description

Engine size

The engine size is the volume of the engine cylinders in which fuel can be combusted. The engine size is measured in litres and is recorded to an accuracy of 0.1L based on the marketing information supplied with each vehicle.

Euro standard The Euro standard is the European emissions standard that the vehicle conforms to. All vehicles used in this thesis conform to either the Euro 5 or

Euro 6 emissions standard.

Fuel type The fuel type is the energy source that is used to propel the vehicle; this is typically either petrol or diesel.

Number of doors

The number of doors is the number of openings on the vehicle that can be used by occupants to access the vehicle. The rear tailgate is also considered as a door, thus vehicles are reported to have either 3 or 5 doors.

Vehicle mass

The vehicle mass is the ‘as tested’ mass of the vehicle and includes the mass of vehicle occupants and monitoring equipment. The mass is recorded in kilograms to the nearest kilogram.

Vehicle power

Vehicle power is the maximum amount of energy the engine is able to produce per unit time. The vehicle power, which is obtained from the marketing material supplied by the vehicle manufacturer, is recorded in brake horsepower to the nearest 1 brake horsepower.

Table 4.3 – vehicle characteristics collected by Emissions Analytics in the metadata

Of the six vehicle characteristics presented in Table 4.3, there are four characteristics that could be used to explain changes in the response variable, mean acceleration. The fuel type and Euro standard are excluded because it is not envisaged that they will influence the mean acceleration of a vehicle. Whilst there may be differences in engine technology due to the fuel type or Euro standard, these are captured in other variables such as engine size and vehicle mass.

Engine size, number of doors, vehicle mass and vehicle power are vehicle characteristics where the influence on vehicle acceleration can be explained. The engine size is related to the amount of fuel that can be combusted on each engine stroke. Therefore, assuming similar levels of efficiency, a vehicle with a larger engine can combust more fuel and thus has more energy to propel the vehicle. The number of doors on the vehicle is a proxy for the aerodynamic properties of the vehicle. Vehicles with a larger frontal area will experience higher resistive forces at high vehicle speeds. Whilst the vehicle speeds in the vicinity of the obstacles investigated is less than 14m/s, there may still be an impact on vehicle acceleration. The vehicle mass will influence acceleration as the heavier the vehicle, the more power that is required to maintain the same rate of acceleration. Finally, the vehicle power is the maximum amount of energy the vehicle can produce per unit time, with a higher power output, a vehicle can accelerate more quickly.

Before the four characteristics can be used as explanatory variables, the composition of each variable needs to be explored to understand the distribution of the data. Table 4.4 shows whether each characteristic is continuous or categorical, summary statistics and the data distribution.

Characteristic Data description Distribution of data

Table 4.4 – composition of the vehicle characteristics that are expected to influence vehicle acceleration

From Table 4.4 it can be seen that the data for each characteristic are not evenly distributed across the ranges observed, this is expected to introduce bias in the model results. However, given the limited number of explanatory variables, it is still proposed that the four characteristics are considered as potential explanatory variables.

Collinearity is the phenomenon where two or more explanatory variables are highly correlated.

Multiple correlated variables in a subsequent statistical model may make interpretation more difficult. The collinearity between two variables can be measured by calculating the correlation coefficient, using either the Pearson product moment or Spearman rank-order. The Pearson product moment is used in this thesis as it relies on the raw data rather than the ranked values for each variable. Table 4.5 shows the collinearity for the four variables: engine size, number of doors, vehicle mass and vehicle power.

Engine size Number of doors Vehicle mass Vehicle power

Engine size 0.145 0.699 0.883

Number of doors 0.312 -0.030

Vehicle mass 0.558

Vehicle power

Table 4.5 – collinearity between the four characteristics expected to influence vehicle acceleration From Table 4.5 it can be seen that correlation is evident between vehicle mass, vehicle power and engine size. This can be explained by the fact that with a larger engine size, more fuel can be combusted on each engine stroke and thus more energy is produced to propel the heavier vehicle.

Also, the larger the physical size of the engine, the heavier it is assuming material choices and engine configuration remain the same. The high correlation between engine size and vehicle power is expected, as a vehicle with a larger volumetric capacity for combusting fuel is able to produce more energy or power assuming similar levels of efficiency.

Considering the results of the collinearity testing, engine size is excluded from the subsequent analysis and the number of doors, vehicle mass and vehicle power are used as the explanatory variables.