### Table 3: High School Non-linear Production Function

in Enhancing our Understanding of the Complexities of Education: "Knowledge Extraction from Data" using

"... In PAGE 18: ... The parsimonious polynomial models paint a somewhat different picture of the predictors of performance for Vermont schools. Table3 displays the significant predictors of SAT performance. While it too selected parent level of education and school size as significant, the shape of the relationship is changed to a third order polynomial for school size.... ..."

### Table 4: Elementary School Non-Linear Production Function

in Enhancing our Understanding of the Complexities of Education: "Knowledge Extraction from Data" using

### Table 4: Average number of Newton iterations for solving the linearized model in non-linear Fair-estimation.

in Solution of Linear Programming and Non-Linear Regression Problems Using Linear M-Estimation Methods

1999

"... In PAGE 109: ...Table4 : Results for the updating routine of the software package when used as a tool for nding L from scratch. Times are given in seconds.... ..."

### Table 1. The Calculated Results for Analyzed Data-Set

2000

"... In PAGE 9: ... In order to have easy interpretable models, we have fixed the maximal number of terms in the equation to be equal to 8 and the maximum degree of polynoms to be equal to 3. The calculations performed using the select params option of the ANALYSIS are summarized in Table1 . The number of stored models was 3.... In PAGE 9: ... It was shown that the use of significant variables, as detected by MUSEUM, = improved PLS results (compare data in column 7 vs. column 6 in Table1 ). The similar tendency was also observed if only variables found to be relevant by the PNN algorithm were used in the cross-validation calculations (compare the last and 7 columns of Table 1).... In PAGE 12: ... b Number of significant PLS components. c The cross-validated q2 calculated using input variables optimized by MUSEUM approach (unless not stated otherwise the PLS results are from Table1 and 15 of (2)). d Number of input variables selected by PNN.... ..."

Cited by 2

### Table 3. Model Fit Errors and Prediction Errors for Non-Linear Process

"... In PAGE 26: ... The fit of all of the models to the data is shown for a 140 point segment in Figure 23. The fit errors (sum of squared residuals) are given in Table3 . Note that the fit error of all the non-linear models and transformed linear model are about equal.... In PAGE 27: ...26 each model. The PRESS numbers are given in Table3 . In this test the FIR model identified using non-linear PLS model was found to have the smallest prediction error, followed by the non-linear PCR model and the polynomial regression.... ..."

### Table 4: Non-linear Test Results

2007

"... In PAGE 12: ... However, for all models, in both time periods, the np test suggests that there is no cointegration, while the kpss test suggests that there is. Table4 presents the results of the various random field based tests for nonlin- earity. For the first time period, 1959-1972, the tests nearly always reject the null hypothesis of linearity.... In PAGE 13: ...odels. The results are interesting and need careful interpretation. The most ob- vious result is that in the second period, it proved impossible to get the numerical optimisation algorithms to converge for Model 1 when no trend was present, and for Model 2 when a trend was present. It is for these two models that the tests for nonlinearity, reported in Table4 , often fail to reject the null hypothesis of linearity. Also, from Table 3, it is the no-trend version of Model 1 that is more likely to be a cointegrating relationship, according to the results of the adf test.... ..."

### Table 1. Empirical Results

"... In PAGE 11: ...INSERT FIGURE 5 (A) TO (F) Empirical Results We present the results of the estimation in Table1 , together with the results of a linear regression of the selected macroeconomic variables on the devaluation probability. The linear regression might also be seen as the estimation of the model presented earlier with Eq.... In PAGE 11: ... The expected signs are, therefore, opposite to those assigned in the case of Jeanne apos;s model. Table1 shows that, for the non-linear case, the level of international reserves is the only variable that is significant and has the expected sign. This points to the importance of this variable in the determination of the fundamental of the Brazilian economy.... In PAGE 12: ...he evolution of the estimated fundamental can be seen in Fig.7. Fig.9 shows the separate contribution of each macroeconomic variable in the composition of the fundamental. One can see clearly the importance of the level of international reserves in this composition, in accordance with the empirical results presented in Table1 . Observing Fig.... ..."

### Table 1. RMSE values for the results obtained with the non-linear model based on neural networks and with the lineal model, for the three considered data series.

"... In PAGE 4: ...s 0.79% whereas for the linear model it is 7.62%. Results for all the three stations are summarized in Table1 . It is shown that the NN non-linear model improves the results obtained with a linear regression model.... ..."

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### Table 3. Comparison of models for the non-linear function approximation.

2003

"... In PAGE 7: ...and validation data set, respectively. Table3 contains comparison results of di erent models for the static function approximation and provides, in addition, re- sults achieved with the neural tree model developed in this paper. It is obvious that the proposed neural tree model worked well for generating an approxi- mating model of the static non-linear system.... ..."

### Table 6 displays the parsimonious non-linear models based on the

"... In PAGE 28: ...Draft as of: 01/17/99 Page 28 of 34 Table6 : Parsimonious Models (GMDH) High School Model Adjusted R 2 = .638 Elementary School Model Adjusted R 2 = .... ..."