A Vector Approach to Regression Analysis and Its Application to Heavy-Duty Diesel Emissions

An alternative approach is presented for the regression of response data on predictor variables that are not logically or physically separable. The methodology is demonstrated by its application to a data set of heavy-duty diesel emissions. Because of the covariance of fuel properties, it is found advantageous to redefine the predictor variables as vectors, in which the original fuel properties are components, rather than as scalars each involving only a single fuel property. The fuel property vectors are defined in such a way that they are mathematically independent and statistically uncorrelated. Because the available data set does not allow definitive separation of vehicle and fuel effects, and because test fuels used in several of the studies may be unrealistically contrived to break the association of fuel variables, the data set is not considered adequate for development of a full-fledged emission model. Nevertheless, the data clearly show that only a few basic patterns of fuel-property variation affect emissions and that the number of these patterns is considerably less than the number of variables initially thought to be involved. These basic patterns, referred to as ''eigenfuels,'' may reflect blending practice in accordance with their relative weighting in specific circumstances. The methodology is believed to be widely applicable in a variety of contexts. It promises an end to the threat of collinearity and the frustration of attempting, often unrealistically, to separate variables that are inseparable.