Regression prediction

Table 4 shows selected results of an ordinary least-squares regression predicting hospital costs... 

J. A. Fernandez Pierna, L. Jin, F. Wahl, N. M. Faber and D. L. Massart, Estimation of partial least squares regression prediction uncertainty when the reference values carry a sizeable measurement error, Chemom. Intell. Lab. Syst., 65, 2003, 281-291. 

Weida storage reservoir —Regression prediction from feeder stream... 

Figure 10.16 Multiple linear regression prediction of olive oil variety from NMR data containing five varieties (at best, all but four predictions are correct with selection by...

Figure 4.4 Multiple regression predicting adaptation in scenario 1 (bold) and scenario 2 (normal font)...

Multiple regression predicting adaptation in scenario 1 (bold)... 

In Table 13, we present the best regression predictions for each kernel. Despite the large number of SVMR experiments we carried out for this QSAR (34 total), the cross-validation statistics of the SVM models are well below those obtained with MLR. 

Another problem is to determine the optimal number of descriptors for the objects (patterns), such as for the structure of the molecule. A widespread observation is that one has to keep the number of descriptors as low as 20 % of the number of the objects in the dataset. However, this is correct only in case of ordinary Multilinear Regression Analysis. Some more advanced methods, such as Projection of Latent Structures (or. Partial Least Squares, PLS), use so-called latent variables to achieve both modeling and predictions. 

The goal of linear regression is to adapt the values of the slope and of the intercept so that the line gives the best prediction of y from x. This is achieved by minimizing the sum of the squares of the vertical distances of the points from the line. An example of linear regression is given in Figure 9-S. 

Partial Least Squares Regression, also called Projection to Latent Structures, can be applied to estabfish a predictive model, even if the features are highly correlated. 

The procedure is as follows first, the principal components for X and Yare calculated separately (cf. Section 9.4.4). The scores of the matrix X are then used for a regression model to predict the scores of Y, which can then be used to predict Y. 

Furthermore, QSPR models for the prediction of free-energy based properties that are based on multilinear regression analysis are often referred to as LFER models, especially, in the wide field of quantitative structure-activity relationships (QSAR). 

Multiple linear regression analysis is a widely used method, in this case assuming that a linear relationship exists between solubility and the 18 input variables. The multilinear regression analy.si.s was performed by the SPSS program [30]. The training set was used to build a model, and the test set was used for the prediction of solubility. The MLRA model provided, for the training set, a correlation coefficient r = 0.92 and a standard deviation of, s = 0,78, and for the test set, r = 0.94 and s = 0.68. 

NMR spectra have been predicted using quantum chemistry calculations, database searches, additive methods, regressions, and neural networks. 

Using a multiple linear regression computer program, a set of substituent parameters was calculated for a number of the most commonly occurring groups. The calculated substituent effects allow a prediction of the chemical shifts of the exterior and central carbon atoms of the allene with standard deviations of l.Sand 2.3 ppm, respectively Although most compounds were measured as neat liquids, for a number of compounds duplicatel measurements were obtained in various solvents. 

The difference between an experimental value and the value predicted by a regression equation. 

Residual error in linear regression, where the filled circle shows the experimental value/, and the open circle shows the predicted value/,. 

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