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

Abstract

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. The available data set is not considered adequate for the 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.

Developing a model for process improvement using multiple regression technique

“…For example, models are developed for predicting hourly ozone concentration (Pai et al, 2010), developing healthy percentage body fat ranges (Gallagher et al, 2000), estimating food consumption of various spices of fish (Palomares and Pauly, 1989), etc. In spite of its reasonably convincing success in many applications, however, the regression approach can face serious difficulties when the independent variables are correlated with each other (McAdams et al, 2000). Multicollinearity or high correlation between the independent variables in a regression equation can make it difficult to correctly identify the most important contributors to a physical process.…”

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

“…The report documents research performed in two phases during 1999 and 2000. Portions were previously published in the technical paper series of the Society of Automotive Engineers (SAE) (McAdams et al, 2000). Section 2 presents the concepts of the vector 7 x .…”

Environmental monitoring of surface ozone and other trace gases over different time scales: chemistry, transport and modeling

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