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. xii EXECUTIVE SUMMARY Multiple regression analysis is one of the most widely used methodologies for expressing the dependence of a response variable on several predictor variables. In spite of its evident success in many applications, the regression approach can face serious difficulties when the predictor variables are to any appreciable extent covariant. This point was made quite evident in a recently published review, which found that efforts to evaluate the separate effects of fuel variables on the emissions from, heavy-duty diesel (HDD) engines were often frustrated by the close association of fuel properties. This report addresses these concerns by offering a new approach to modeling the effects of fuel characteristics on emissions. The work was motivated by the observation that most HDD engine research was conducted with test fuels that had been "concocted'.' in the laboratory to vary selected fuel properties in isolation from each other. This approach can eliminate the confounding effect caused by naturally covarying fuel properties, but it departs markedly from the real world, where the reformulation of fuels to reduce emissions will naturally and inevitably lead to changes in a series of interrelated properties. What impact might this method of blending test fuels have on their ability to provide an accurate and reliable basis for assessing the emissions performance of future diesel fuels? Development of a New Statistical Methodology The approach presented here is based on the use of Principal C...