Standardized partial regression coefficient

The standardized partial regression coefficient t is a measure of the relative importance of the corresponding predictor and is given by... 

The second advantage of the present procedure is that we can now readily obtain the standard error of each partial regression coefficient. We need the residual variance vr which we already have in Table 10.1. To repeat, in the present symbolism, it is 1... 

With the aim of bringing the regression coefficients a and P into a common scale, Krygowski and Fawcett calculated the partial regression coefficients a and p by the standard method of multi-parameter regression. From these they obtained... 

A number of variable selection techniques were also suggested for the Partial Least Squares (PLS) regression method [Lindgren et al, 1994]. The different strategies for PLS-based variable selection are usually based on a rotation of the standard solution by a manipulation of the PLS weight vector w or of the regression coefficient vector b of the PLS closed form. 

Regression coefficients, partial, 172 standardized, 168 Regression, linear, 156 multivariate, 171 polynomial, 163 through origin, 162 Residuals, 13 Residuals analysis, 159 Ridge regression, 203 RMS noise, 31 Roots, characteristic, 73... 

SE Standard error, R coefficient of determination, SEC standard error of calibration, SEV(C) standard error of cross-validation, PLS terms number of terms used for modified partial least squares regression. 

Standardized regression coefficient Effect size (partial eta squared]... 

The t statistic is sometimes referred to as the ratio of the actual regression coefficient for a particular wavelength to the standard deviation of that coefficient. The partial F value described is equal to this t value squared noting that the t value calculated this way retains the sign of the coefficient, whereas all F values are positive. 

Table 3 (73) compares the retention coefficients for synthetic peptides from various sources. To ensure comparability, the data has been standardized with respect to lysine and assigned a value of 100. The table shows that there are discrepancies between the results obtained using different chromatographic systems. Predictions of retention times should therefore be made using chromatographic systems similar to those used to calculate the retention coefficients for the amino acids. Casal et al. (75a) have made a comparative study of the prediction of the retention behavior of small peptides in several columns by using partial least squares and multiple linear regression analysis. 

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