Errors mean square

The problem with plant data becomes more significant when sampling, instrument, and cahbration errors are accounted for. These errors result in a systematic deviation in the measurements from the actual values. Descriptively, the total error (mean square error) in the measurements is... 

The root-mean-square error is the square root of the mean square error. Note that since the root-mean-square error involves the square of the differences, outliers have more influence on this statistic than on the mean absolute error. 

Which measure of scatter is likely to be larger, the mean absolute error or the root-mean-square error ... 

The unknown parameters of the model, such as film thicknesses, optical constants, or constituent material fractions, are varied until a best fit between the measured P and A and the calculated P/ and A/ is found, where m signifies a quantity that is measured. A mathematical function called the mean squared error (MSE) is used as a measure of the goodness of the fit ... 

This argument obviously can be generalized to any number of variables. Equation (2-65) describes the propagation of mean square error, or the propagation of variances and covariances. 

The root-mean-square error (RMS error) is a statistic closely related to MAD for gaussian distributions. It provides a measure of the abso differences between calculated values and experiment as well as distribution of the values with respect to the mean. 

Figure 16 Root-mean-squared error progression plot for Fletcher nonlinear optimization and back-propagation algorithms during training.

The Mean Squared Error of Prediction (MSEP) is supposed to refer uniquely to those situations when a calibration is generated with one data set and evaluated for its predictive performance with an independent data set. Unfortunately, there are times when the term MSEP is wrongly applied to the errors in predicting y variables of the same data set which was used to generate the calibration. Thus, when we encounter the term MSEP, it is important to examine the context in order to verify that the term is being used correctly. MSEP is simply PRESS divided by the number of samples. 

It is quite a simple matter to generalize the simple prediction problem just discussed to the situation where we want to obtain the best (in the sense of minimum mean square error) linear estimate of one random variable fa given the value of another random variable fa. The quantity to be minimized is thus... 

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. 

Root mean square error Mean of response Observations (or sum wt)... 

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%.

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. 

The equation assumes that the cost of estimation error for an estimate based on n replicate samples is proportional to the mean squared error... 

Statishcal criteria of Eq. (24) are too good the standard deviation, which was created on the basis of different measurements by various authors, is much less than even the experimental error of determinahon. This could be due to mutual intercorrelation of descriptors leading to over-ophmistic statistics [18]. Another reason may be the lack of diversity in the training set. The applicahon of the solvation equation to data extracted from the MEDchem97 database gave much more modest results n = 8844, = 0.83, root mean square error = 0.674, F = 8416... 

Optimization of the PPR model is based on minimizing the mean-squares error approximation, as in back propagation networks and as shown in Table I. The projection directions a, basis functions 6, and regression coefficients /3 are optimized, one at a time for each node, while keeping all other parameters constant. New nodes are added to approximate the residual output error. The parameters of previously added nodes are optimized further by backfitting, and the previously fitted parameters are adjusted by cyclically minimizing the overall mean-squares error of the residuals, so that the overall error is further minimized. 

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