Stepwise multiple linear regression

Some of the earliest applications of chemometrics in PAC involved the use of an empirical variable selection technique commonly known as stepwise multiple linear regression (SMLR).8,26,27 As the name suggests, this is a technique in which the relevant variables are selected sequentially. This method works as follows ... 

For the biotransformation assay results, concentration-normalized maximum induction values were modeled. Stepwise multiple linear regression analysis was used to select the most suitable parameters from log Kow, EHOMO, ELUMO, and the difference in EHOMO and ELUM0 (ELUM0 - EH0M0). 

These later two models of bioavailability as a continuous variable are linear since they used stepwise multiple linear regression (M LR) as the modeling tool. An obvious alternative, which may offer improved performance, is a nonlinear technique and such a model using an artificial neural network (ANN) was reported by Turner and colleagues [30], This study employed 167 compounds characterized by several descriptor types, ID, 2D, and 3D, and resulted in a 10-term model. Although the predictive performance was judged adequate, it was felt that the model was better able to differentiate qualitatively between poorly and highly bioavailable compounds. 

Statistical Analysis. Stepwise multiple linear regression analysis was used to determine the measured soil properties most correlated with EDB residues and to formulate a predictive equation to estimate chemical concentration. The regression analysis was performed on results from location 1 (Table IV) only because the number of segments containing residues at location 2 were not sufficient to produce an analysis. 

There are two stepwise multiple linear regression analyses that have derived a mathematical formula for determining a lithium dose based on a number of dependent variables. 

In the NIRS technique, the spectra need to be processed by using either principal component regression (PCR), multiple linear regression (MLR), stepwise multiple linear regression (SMLR), maximum... 

None of the above approaches optimizes the relationship between NIR absorbances and analyte for a range of sample types. Derivative transformations have been found to be generally useful when stepwise multiple linear regression (SMLR) techniques are used. When multidimensional statistics are employed, e.g., partial least-squares (PLS), principal component regression (PCR), or neural nets, it has been observed in some cases that the untransformed log 1/R data can perform just as well in correlation coefficient and error terms as in any kind of transformation. It is considered that in some cases physical manifestations of the sample contained in the spectra provide valid and useful discriminant data. 

Stepwise multiple linear regression. This is a modified form of forward selection. The model starts out including only one variable, and more variables are subsequently added. But at each stage a BE-style test is also applied. If a variable is added, but becomes less important as a result of subsequent additions, SMLR will allow its removal from the model. 

Besides stepwise multiple linear regression (MLR) analysis, other methods used for deriving QSAR models were E-state modeling [168], kNN based COMBINE [173] and VALIDATE [I8I], The VALIDATE method makes use of 3D-coordinates of known ligand-receptor complexes to calculate physicochemical parameters. It was one of the very few studies where QSAR was part of the design and synthetic efforts [181]. Several statistical techniques such as stepwise regression, EA-MLR, PCRA and PLS analysis were applied in a recent study [194] to identify the structural and physicochemical requirements for HIV protease inhibitory activity. 

Vector containing regressors Residual in X matrix after a factors Residual in y vector after a factors Root mean squares of error prediction Partial least-squares regression Principal component regression Stepwise multiple linear regression PLSR with only one y-variable... 

A major application of NIR in the polymer industry is compositional analysis. Identification of different polymers, their properties, and their morphological differences normally requires extensive testing and complicated, time-consuming analysis. A difficulty with polymer applications is that it is not easy to create a stable calibration with stepwise multiple linear regression analysis because the constituent of interest may show little variation and, as a result, regression coefficients tend to have small values. 

Du Toil et al. (2007) determinated the antibacterial activity of thirteen homoisoflavanones isolated from six Hyacinthaceae species against Staphylococcus aureus. They also developed a set of physicochemical parameters that would describe antibacterial activity for these and future compounds. Stepwise multiple linear regression analysis of the data yielded a statistically significant two-component model (R = 0.81, p < 0.003). 

MLR = multiple linear regressions PCA = principal components analysis PLS = partial least squares SMLR stepwise multiple linear regression. 

The experimental retention factors were determined by reversed-phase high-performance liquid chromatography HPLC). Stepwise multiple linear regression (MLR) and partial least square (PLS) methodology were used to investigate the correlation between the retention factor and a number of molecular descriptors for these compounds. The MLR and PLS equations were found to be useful for the estimation and comparison of retention factors k ) for new synthesized phosphoramidic acid derivatives using the selected molecular descriptors. More details are given in the section on HPLC. 

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