Relative root mean-square error

The AcoustoSizer software assumes that the size follows a lognormal distribution and adjusts the median and spread of the distribution, along with the zeta potential, to give the best fit to the mobility spectrum, by minimizing the relative root mean square error (superscript th is the theoretical) ... 

Note RMSE, root-mean-square error REP, relative root-mean-square error. 

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. 

RRMSE = Relative root mean square error. 

Figure 9. Linearity of response and reproducibility. The error flags indicate the root mean square error for five measurements at each value. The average relative error is about 10%.

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). 

It is a straightforward matter to fit various model profiles to realistic, exact computed profiles, selecting a greater or lesser portion near the line center of the exact profile for a least mean squares fit. In this way, the parameters and the root mean square errors of the fit may be obtained as functions of the peak-to-wing intensity ratio, x = G(0)/G(comax)- As an example, Fig. 5.8 presents the root mean square deviations thus obtained, in units of relative difference in percent, for two standard models, the desymmetrized Lorentzian and the BC shape, Eqs. 3.15 and 5.105, respectively. 

Predict die eight responses using y = D.b and calculate the percentage root mean square error, adjusted for degrees of freedom, relative to the average response. 

Relative error in calculation. The relative error calculated from the root mean square error in calculation, defined as... 

Another example of applying chemometrics to separations data is depicted in Figures 8 and 9. Here, interval PLS (iPLS) was applied to blends of oils in order to quantify the relative concentration of olive oil in the samples (de la Mata-Espinosa et al., 2011b). iPLS divides the data into a number of intervals and then calculates a PLS model for each interval. In this example, the two peak segments which presented the lower root mean square error of cross validation (RMSECV) were used for building the final PLS model. 

The experiments are taken with Weka machine learning package, and the results are evaluated by several statistical metrics. We provide an explanation of these parameters in the following parts. The statistical metrics of the predictive results are evaluated by accuracy, Kappa statistics, mean absolute error, root mean squared error, and relative absolute error. For the prediction performance, we normally refer to accuracy, which is the... 

An exclusively computational method for obtaining enolization equilibrium constants in water has been described, based on gas-phase free energy changes, solvation energies and a correction for the latter via a parameterization scheme. In some cases where computed and experimental values disagree, the authors identify concerns with the experimental values. For 37 reactions, the correlation shows a root-mean-square error of 1.3 kcal mol . The report includes an examination of the relative stability of some E- and Z-enols. 

The quality of developed PLS model was evaluated by cross-validation technique. The values of root mean square error of cross validation obtained are relatively low, 1.68% and 1.32% (volume/volume), respectively for com oil and sunflower. Based on this result, the method developed has a good ability to estimate the percentage of com oil and sunflower as oil adulterants in virgin eoconut oil samples. 

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