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 engines were often frustrated by the close association of fuel properties. Most research on heavy-duty diesel engines has been conducted with test fuels that have 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.
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