Root-mean-square error of calibration

Root mean square (RMS) granularity, 19 264 Root-mean-squared error of cross-validation (RMSECV), 6 50-51 Root-mean-squared error of calibration (RMSEC), 6 50-51... 

RMSEC root mean square error of calibration... 

Root Mean Square Error of Calibration (RMSEC) Plot (Model Diagnostic) The RMSEC as a function of the number of variables included in the model is shown in Figure 5-77. It decreases as variables are added to the model and the largest decrease is observed between a one- and two-variable model. The reported error in the reference caustic concentration is approximately 0.033 vrt.% (la). The tentative conclusion is that four variables are appropriate because the RMSEC is less than the reference concentration error after five variables are included in the model. 

Root mean square error of calibration (RMSEC). 255 of cross validation for PC.A (RMSEC PCA). 93-94 of prediction IRMSEP) in DCLS. 200- 201 idealized behavior. 2SS-289 in MLR, 255 in PLS, 287-290 Row space, 58-59 Rsquare. 253 adjusted. 253... 

Root mean square error of calibration (RMSEQ plot (RMSEC vs. number of variables)... 

The simplest approach to determining the number of significant components is by measuring the autoprediction error. This is also called the root mean square error of calibration. Usually (but not exclusively) the error is calculated on the concentration data matrix (c), and we will restrict the discussion below to errors in concentration importantly, similar equations can be obtained for the x data. 

The simplest approach to determining number of significant components is by measuring the autoprediction error. This is the also called the root mean square error of calibration. 

The results with PCR and PLS regression include the number of PCs obtained by leave-one-out cross-validation procedure, the values of regression coefficients for X variables, the value of R, and the root mean square error of calibration (RMSE C ) and the root mean square error of prediction by cross-validation proce-... 

NC = number of components selected by cross-validation, = determination coefficient, RMSEC = Root Mean Square Error of Calibration, RMSEP = Root Mean Square Error of Prediction... 

Table 1. Comparison of three PLS models in the Slurry-Fed Ceramic Melter data set. The variance in both blocks of data and the Root Mean Square Error of Calibration (RMSEC), Cross-validation (RMSECV) and Prediction (RMSEP) are compared.

The developed models should be tested using independent samples as validation sets to verify model accuracy and robustness. To evaluate model accuracy, the statistics used were the coefficient of correlation in calibration (rc i), coefficient of correlation in prediction (rpred), root mean square error of calibration (RMSEC), and root mean square error of prediction (RMSEP). 

This method was in fact carried out around two decades ago [30, 31]. However, it was applied only in the fermentation of pure microbial cultures. In a recent report by Acros-Hernandez and coworkers [32], infrared spectroscopy was applied to quantify the PHA produced in microbial mixed cultures. Around 122 spectra from a wide range of production systems were collected and used for calibrating the partial least squares (PLS) model, which relates the spectra with the PHA content (0.03-0.58 w/w) and 3-hydroxyvalerate monomer (0-63 mol%). The calibration models were evaluated by the correlation between the predicted and measured PHA content (R ), root mean square error of calibration, root mean square error of cross validation and root mean square error of prediction (RMSEP). The results revealed that the robust PLS model, when coupled with the Fourier-Transform infrared spectrum, was found to be applicable to predict the PHA content in microbial mixed cultures, with a low RMSEP of 0.023 w/w. This is considered to be a reliable method and robust enough for use in the PHA biosynthesis process using mixed microbial cultures, which is far more complex. 

The RMSNV allows the evaluation of the trends and distance from target concentrations for not only the achve pharmaceutical ingredient, but also the major excipients of the formulation. In the original paper, the endpoint was determined based on the distribution of RMSNV values. In Zacour et al. [30], the root mean square error of calibration for the components of interests was used as the threshold under which the blend was determined homogeneous. 

Optimal root mean squared error of calibration. 

The root mean square error of calibration (RMSEC) measures the average difference between the predicted and the reference values and, thus, gives an overall view of the fit of the model (how well the model predicts the same samples that were used to calculate the model). It is calculated as RMSEC = [E(y-yi.eference) /(f— — l)], whcrc I and A have the usual meanings, and the 1 takes account of the mean-centring or autoscaling of the... 

The root mean squared error of calibration (RMSEC) has been defined above. The leverage, ha, quantifies the distance of the predicted sample (at zero concentration level) to the mean of the calibration set in the -dimensional space Hq can be estimated as an average value of the leverages of a set of validation samples having zero concentration of the analyte. For a model calculated from mean-centred spectra its calculation was presented in Section 5.3 in matrix notation /zo=l//+to (T T) 4o, where to is the (.4x1) score vector of the predicted sample and T is the (7x4) matrix of scores for the calibration set. Finally, A(a,p,v) is a statistical parameter that takes into account the a and (3 probabilities of falsely stating the presence/absence of analyte, respectively, as recommended elsewhere. When the number of degrees of freedom i.e. the number of calibration samples) is high (v>25), as is usually the case in multivariate calibration models, and a =) , then A(a,(S,v) can be safely approximated to 2 ... 

Figure 6.7 The root mean square error of calibration (RMSEC), leave-one-out cross validation (RMSECV) and prediction (RMSEP) are plotted as a function of the signal-to-noise ratio (SNR). While the intrinsic SNR amounts to 3000, random noise was artificially added to mid-IR spectra of 247 serum samples (which decreases the SNR) and the concentration of glucose was recalculated by means of partial least squares (PLS) based on the noisy spectra. The open symbols refer to assessing the quality of quantification within the teaching set, while the filled symbols relate to an external validation set. The data show that the noise can be increased by more than an order of magnitude before the prediction accuracy of the independent external validation set (RMSEP) is affected. In addition, it can clearly be observed that the RMSEC is a poor measure of accuracy since it suggests delivering seemingly better results for lower SNRs, while in fact the calibration simply tends to fit the noise for low values of SNR (see section 6.7).

In GA-PLS, model vahdation was achieved through leave-one-out cross-validation (LOO CV) to find the best number of latent variables (Lv) to be used in calibration and prediction. External validation (for a test set), and the predictive ability was statistically evaluated through the root mean square errors of calibration (RMSEC) and vahdation (RMSECV). The results indicate that four latent variables are the best number to make a model. The following equation represents the best model achieved by GA-PLS ... 

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