# residual sum of squares

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## residual sum of squares

[rə¦zij·ə·wəl ¦səm əv ′skwerz]
(statistics)
McGraw-Hill Dictionary of Scientific & Technical Terms, 6E, Copyright © 2003 by The McGraw-Hill Companies, Inc.
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coefficient of determination (0.994 and 0.996 R2 for Hd and Hm), Generalized Cross Validation (0.000038 and 0.024024 GCV for Hd and Hm), Cross-Validation R2 (0.974 and 0.967 CVR2 for Hd and Hm), Residual Sum of Squares (0.00046 and 0.28829 RSS for Hd and Hm) and Standard Deviation Ratio (0.078 and 0.063 SDRATIO for Hd and Hm) were calculated for penalty= -1 in the package "earth" of the R software.
To this end, we employed a residual sum of squares error approach to compare the library preparation methods.
The partial [R.sup.2] of hospital's prior ARR is calculated as one minus the ratio of the residual sum of squares from specification (a) and the residual sum of squares from specification (c).
The comparative analysis between the linear regression model and non-linear regression one (in our study being a parabola type) regarding the relation of determination of pulmonary pressure in hyperthyroidism shows that the polynomial model is better than the linear one in all situations because a) the coefficients of determination R2 are higher; b) residual sum of squares for polynomial regression are smaller than the residual sum of squares for linear regression highlighting the fact that the difference between the measured values and the values obtained through the polynomial model (values on the curve) are lower; c) DAIC has negative values and the more complicated model (parabola type one) is considered to be better.
According to ICH, linearity parameters that should be estimated are slope, intercept, correlation coefficient, and residual sum of squares. As tabulated above, the correlation coefficient was closer to unity (>0.997).
Fluorescence data were analyzed using matrix feature extraction method based on alternating trilinear decomposition (ATLD) and residual sum of squares, combining the threshold to judge the unknown samples and to detect the aqueous samples of organic contaminants.
Residual sum of squares of the optimal in-season model was lower than that of the pre-season forecast (sibling) model, indicating the former was more accurate than the latter.
The degree of adjustment of each model was verified considering the magnitude of the adjusted coefficient of determination ([R.sup.2]), standard deviation of estimate (SE), residual sum of squares (RSS) and the tendency of residual distribution (Goneli et al., 2011; Reis et al., 2011; Moraes et al., 2013).
Where SSR and SST are the residual sum of squares and total sum of squares respectively.
The literature is quite rich in algorithms for the minimization of residual sum of squares in nonlinear model situations.
This is simply a normalized residual sum of squares and normalizing quantity v, sometimes known as the degrees of freedom, which is given by v = n - 2[[SIGMA].sub.i]w[x.sub.i,h]([X.sub.i]) + [[SIGMA].sub.i,h] [w.sup.2] [x.sub.j,h]([X.sub.i]).
Generally use K-fold cross-validation method to calculate prediction residual sum of squares to determine the number of components extracted, reaching the purpose of dimension reduction.

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