RMSE, Root Mean Square Error 71, Figur

Figure 2. Root Mean Square Error (RMSE). Target 1...

Figures 11 and 12 illustrate the performance of the pR2 compared with several of the currently popular criteria on a specific data set resulting from one of the drug hunting projects at Eli Lilly. This data set has IC50 values for 1289 molecules. There were 2317 descriptors (or covariates) and a multiple linear regression model was used with forward variable selection the linear model was trained on half the data (selected at random) and evaluated on the other (hold-out) half. The root mean squared error of prediction (RMSE) for the test hold-out set is minimized when the model has 21 parameters. Figure 11 shows the model size chosen by several criteria applied to the training set in a forward selection for example, the pR2 chose 22 descriptors, the Bayesian Information Criterion chose 49, Leave One Out cross-validation chose 308, the adjusted R2 chose 435, and the Akaike Information Criterion chose 512 descriptors in the model. Although the pR2 criterion selected considerably fewer descriptors than the other methods, it had the best prediction performance. Also, only pR2 and BIC had better prediction on the test data set than the null model.

Experimental values obtained in this way must be compared with those calculated according to Equation (21). Predicted versus experimental values are compared in Figure 10. The root mean square error (RMSE) is less than 5.6%. It should be noted that no adjustable parameters have been employed and the method can be used for any reacfor size without limitations. 

Figure 9.2 The root mean squared error (RMSE) of models for prediction of aqueous solubility of chemical compounds shown as a function of the number of molecules, n, used for model development and validation. The results of methods developed using quantum chemical (3D), topological descriptors (2D/1D), and methods based on other physicochemical descriptors (PhysChem) are shown.

Figure 10.38. Residual plots of (a) the stationary phases and (b) all mobile-phase/solute combinations. Legend RMSE stands for root-mean-squared error (see text) and the dotted line indicates the mean RMSE for the whole data set.

FIGURE 34.5 Cross-validated predicted versus measured plots for rapeseed methyl ester (RME) in jet fuel (ppm). The root mean square error (RMSE) is 2.2. ppm. Adapted from Eide et al. [13]. 

Subsequently, the deviation of data points around each continuous p>ath can be calculated by various methods such as coefficient of determination (R2), Root Mean Square Error (RMSE) or Percent of Absolute Error (PAE). The PAE values of continuous paths on xi-y and X2-y planes (figures 2e and 2f) are 20.4 and 13.5%, respectively (Step 4). 

Figure 6.13 The root mean square error (RMSE) as derived from the calibration within the teaching set (RMSEC) or from evaluating the independent validation set (RMSEP) as a function of the ratio between the number of samples used to teach the algorithm and the number of parameters (latent variables) 5, 10, or 20 samples out of the teaching set were used for teaching. The dashed line indicates that the ratio should be larger than 5 in order to obtain reasonable values for independent validation. For Nteach/Npara < 5 the RMSEC decreases due to overfitting, but the RMSEP reveals that in fact only random variations had been fitted, which were not found in the independent validation set.

Figure 28.4b, the variables selected by MLR-SPA are indicated. Table 28.1 also contains the root-mean square error (RMSE) and relative root-mean-square error (REP) for the calibration models and validation set, respectively. 

The training set is used to build the N-PLS model, which will then be validated using the test set samples. When building the model, one of the first decisions to be taken is the optimal number of PLS factors to be included here, the choice is made on the basis of the root-mean-square error (RMSE) in cross-validation (seven cancellation groups), which is reported in Figure 17 as a function of the number of components. 

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