Creating multiple regression models

Creation of a simple linear regression equation is obvious there are just two variables involved and all that is required is the estimation of the slope and intercept parameters, usually by OLS. The construction of multiple linear regression equations, on the other hand, is by no means as clear since the selection of independent variables for the equation involves choice. How can this choice be made One obvious strategy is to use all of the independent variables and this in fact is the basis of one technique for 

The individual regression equations between p/50 and the two n-electron density parameters have quite reasonable correlation coefficients and thus it might be expected that they would be useful in a multiple regression equation. The two equations, however, are almost identical, indicating a very high collinearity between these descriptors. When combined into a two-term equation (eqn 6.20), which has an improved correlation coeffi- 

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A linear mathematical function that relates descriptor values to a biological activity can be created using multiple linear regression. For n observations and p independent variables the general linear regression model is represented as... 

FIGURE 4.24 PLS as a multiple linear regression method for prediction of a property y from variables xi,..., xm, applying regression coefficients b1,...,bm (mean-centered data). From a calibration set, the PLS model is created and applied to the calibration data and to test data. 

In this paper the PLS method was introduced as a new tool in calculating statistical receptor models. It was compared with the two most popular methods currently applied to aerosol data Chemical Mass Balance Model and Target Transformation Factor Analysis. The characteristics of the PLS solution were discussed and its advantages over the other methods were pointed out. PLS is especially useful, when both the predictor and response variables are measured with noise and there is high correlation in both blocks. It has been proved in several other chemical applications, that its performance is equal to or better than multiple, stepwise, principal component and ridge regression. Our goal was to create a basis for its environmental chemical application. 

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