Root mean square prediction error

For the data the squared correlation coefficient was 0.93 with a root mean square error of 2.2. The graph of predicted versus actual observed MS(1 +4) along with the summary of fit statistics and parameter estimates is shown in Figure 16.7. 

Aptula AQ, Jeliazkova NG, Schultz TW, Cronin MTD. The better predictive model high q for the training set or low root mean square error of prediction for the test set QSAR Comb Sci 2005 24 385-96. 

We have compared one-step and two-step ahead scheduling using two performance measures. The first is the root mean square error of the track estimation this is a fairly obvious measure of the performance of the tracker. The second measure was the number of track updates. Since the sensor is managed in such a way that track updating is done only when the predicted track error exceeds a threshold, this also gives a measure of how far the estimation process is diverging from the actual target state. 

Root-mean-squared error of prediction (RMSEP), 6 50-51... 

The root mean squared error (RMSE) is the square root of MSE, and can again be given for calibration (RMSEC or RMSECAL), CV (RMSECV or RMSECv) or for prediction/test (RMSEP, or RMSEtest). In the case of a negligible bias, RMSEP and SEP are almost identical, as well as MSEniST and SEP2. 

The pilot study showed good prospects for predicting crystallization point temperatures directly from the acoustic signatures of the liquid feed into the granulator with an indicated prediction error (root mean square error of prediction) RMSEP = 1.1 °C. 

Chemometrics in Process Analytical Technology (PAT) 409 The main figure of merit in test set validation is the root mean square error of prediction (RMSEP) ... 

NIR models are validated in order to ensure quality in the analytical results obtained in applying the method developed to samples independent of those used in the calibration process. Although constructing the model involves the use of validation techniques that allow some basic characteristics of the model to be established, a set of samples not employed in the calibration process is required for prediction in order to conhrm the goodness of the model. Such samples can be selected from the initial set, and should possess the same properties as those in the calibration set. The quality of the results is assessed in terms of parameters such as the relative standard error of prediction (RSEP) or the root mean square error of prediction (RMSEP). 

Additional examination of the model s fit is performed through the comparison of the experimental and predicted bioactivities and is needed to statistically ensure that the models are sound. The methods of chi (%) and root-mean squared error (RMSE) are performed to determine if the model possesses the predictive quality reflected in the R2. The use of RMSE shows the error between the mean of the experimental values and predicted activities. The chi value exhibits the difference between the experimental and predicted bioactivities ... 

Root Mean Square Error of Prediction (RMSEP) Plot (Model Diagnostic) The validation set is employed to determine the optimum number of variables to use in the model based on prediction (RMSEP) rather than fit (RMSEO- RM-SEP as a function of the number of variables is plotted in Figure 5.7S for the prediction of the caustic concentration in the validation set, Tlie cuive levels off after three variables and the RMSEP for this model is 0.053 Tliis value is within the requirements of the application (lcr= 0.1) and is not less than the error in the reported concentrations. 

Root Mean Square Error of Prediction (RMSEP) Plot (Model Diagnostic) The new RMSEP plot in Figure 5-100 is more well behaved than the plot shown in Figure 5-93 (with the incorrect spectrum 3). A minimum is found at 3 factors with a corresponding RMSEP that is almost two orders of magnitude smaller than the minimum in Figure 5-93- The new RMSEP plot shows fairly ideal behavior with a sharp decrease in RMSEP as factors are added and then a slight increase when more than three factors are included. 

Root mean square error of prediction OtMSEP) plot (RMSBP vs. number of factors)... 

RMSEP. see Root mean square error, of prediction... 

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 Cross Validation for PCA Plot (Model Diagnostic) As described above, the residuals from a standard PCA calculation indicate how the PCA model fits the samples that were used to construction the PCA model. Specifically, they are the portion of the sample vectors that is not described by the model. Cross-validation residuals are computed in a different manner, A subset of samples is removed from the data set and a PCA model is constructed. Then the residuals for the left out samples are calculated (cross-validation residuals). The subset of samples is returned to the data set and the process is repeated for different subsets of samples until each sample has been excluded from the data set one time. These cross-validation residuals are the portion of the left out sample vectors that is not described by the PCA model constructed from an independent sample set. In this sense they are like prediction residuals (vs. fit). 

Root Mean Square Error of Prediction (RMSEP) (Model Diagnostic) The RMSEP for the determination of caustic is 0.06 wt.% over a range of 7.4-10.4 wt.%. This estimate of prediction ability indicates that the performance of the model is acceptable for the application. 

Root Mean Square Error of Prediction (RMSEP) Plot (Model Diagnostic) Prediction error is a useful metric for selecting the optimum number of factors to include in the model. This is because the models are most often used to predict the concentrations in future unknown samples. There are two approaches for generating a validation set for estimating the prediction error internal validation (i.e., cross-validation with the calibration data), or external validation (i.e., perform prediction on a separate validation set). Samples are usually at a premium, and so we most often use a cross- validation approach. 

Root Mean Square Error of Prediction (RMSEP) Plot (Model Diagnostic) The RMSEP versus number of factors plot in Figure 5.113 shows a break at three factors and a leveling off after six factors. Tlie RMSEP value with six factors (0,04) is comparable to the estimated error in the reported concentrations (0.033), indicating the model is predicting well At this point we tentatively choose a rank six model. The rank three model shows an RMSEP of 0.07 and may well have been considered to be an adequate model, depending on how well the reference values are known. 

Root Mean Square Error of Prediction (RMSEP) Plot (Model Diagnostic) The RMSEP plot for the MCB model is shown in Figure 5.127. Although the shape of this RMSEP plot is not ideal, it does not exhibit erratic behavior. Tlie first minimum in this plot is at four factors with a lower minimum at six factors. In Section 5.2.1.2, nonlinear behavior was suspected as the root cause of the failure of the DCLS method. Tlicreforc, it is reasonable that a PLS model re-... 

The first PC quantified the moisture content as evident from the strong contribution around 1930 nm region, which represents the combination band of the -OH stretching and -OH bending vibrations. The second PC quantified the baseline shift due to changing sample density as a result of changing compression pressures. The third PC quantified the changes in MCC structure as evident from its resemblance with NIR spectrum collected on the 100% MCC powder sample. The root mean-square errors of prediction for different sample properties are summarized in Table 14. 

Table 14 Root Mean Squares Errors for the NIR-PLS Predicted Values of Different Sample Attributes for the MCC Surrogate Tablets and Roller Compacted Samples...

The new samples constitute what is called the validation set and, of course, the more validation samples you have, the more representative the conclusions will be. The RMSEP (root mean square error of prediction) statistic measures how well the model predicts new samples. It is calculated as... 

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