Regression analysis model refinement

This example was first introduced by Gorman and Toman (1966) and since then was extensively used in the statistical literature. The data set contains 36 data points of 10 dependent variables and one independent variable, where each row in the data set represents one day of operation of a petroleum refining unit. The complete data set of this example is given in Daniel and Wood (1980). They have also carried out a stepwise regression analysis of the data set using a linear model that includes a free parameter and the transformation In y for the dependent variable. This corresponds to Step 1 of the proposed algorithm with A = 0. The optimal solution obtained for this case by SROV is shown in Table 1. Note that the range of the dependent variable, the parameter values... 

Multivariate models have been successful in identifying source contributions in urban areas. They are not independent of Information on source composition since the chemical component associations they reveal must be verified by source emissions data. Linear regressions can produce the typical ratio of chemical components in a source but only under fairly restrictive conditions. Factor and principal components analysis require source composition vectors, though it is possible to refine these source composition estimates from the results of the analysis (6.17). 

Quantitative analysis for one or more analytes through the simultaneous measurement of experimental parameters such as molecular UV or infrared absorbance at multiple wavelengths can be achieved even where clearly defined spectral bands are not discernible. Standards of known composition are used to compute and refine quantitative calibration data assuming linear or nonlinear models. Principal component regression (PCR) and partial least squares (PLS) regression are two multivariate regression techniques developed from linear regression (Topic B4) to optimize the data. 

At thi s point, the fit of the model to the data must be evaluated caiefiiUy, since it was not possible to perform an initial graphical analysis. Residual plots should constructed to identify any systematic errors between the data and the model. For this example, at least four residual plots are appropriate, i.e., plots of the residuals in —rA versus Ca, Cb, Cc, and Cd. A parity plot should also prepared to allow a visual conqiarison of the model and the data, and to permit outlying points to be identified. Finally, the parameter estimates should be refined via nonlinear regression. 

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