The expected value of the mean squared prediction error for our classification into k classes for some sample size N was computed here using:

Comparison of mean squared prediction error between conventional soil mapping and DSM

Explained variance by Explained variance by original quadratic PLS robust quadratic PLS Contamination rate X Y X Y 5% 0.99 0.73 1 0.99 10% 1 0.68 1 0.99 15% 1 0.67 1 0.99 TABLE 3: Comparison between optimal

mean squared prediction error and predictive error sum of squares of proposed quadratic algorithm and original one for simulated dataset with three contamination rates (5%, 10%, and 15%).

Mean squared prediction error (MSPE) was split into squared bias (SB), systematic error (SE) and random error (RE), according to Bibby and Toutenburg (1977).

(MAD), MAD = [[summation].sup.n.sub.i=1] [absolute value of [Y.sub.i] [[??].sub.i]]/n mean squared prediction error MSPE = [[summation].sup.n.sub.i=1] [absolute value of[ ([Y.sub.i] [[??].sub.i]).sup.2]/n

For milk production, the lowest values for the residual mean square (RME), mean absolute deviation (MAD), mean squared prediction error (MSPE) and Index, were observed through Brody II followed by QLF and LHF (Table 1).

In turn, Tedeschi (5) conducted a review of various techniques to evaluate mathematical models designed for predictive purposes: linear regression analysis, adjusted errors analysis, concordance correlation coefficient, several evaluation measurements,

mean squared prediction error, non-parametric analysis and comparison of the distribution of the data observed and predicted.

Predictive performance of the model was assessed by calculating the mean error (predicted-observed concentration) and its 95% confidence interval (CI) as an estimate of bias, and the root mean squared prediction error and 95% CI as an estimate of precision.

Predictive performance of final model established in the validation group Final model Error 4.88 (2.73-7.02) Mean prediction error (MPE) 2.21 (2.17-2.26) Mean squared prediction error (MSPE) 1.48 (0.39-1.53) Root mean sqaured prediction error (RMSE)

Appendix A shows a two-step breakdown of mean squared prediction error (MSE).

Panel A: Partition of Mean Squared Prediction Error

If [[pi].sub.i], denotes the relative area of the ith class out of k and N is the total number of observations, then the expected value of the

mean squared prediction error for classes is: