### 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: 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 4: Comparison of the proposed method and ordinary linear and non-linear regression when 35% unexplained variance added to the response variable and all driving attributes used for model training

2000

"... In PAGE 6: ... Similar results were obtained when attribute noise was added. However, when the proposed method was applied on data with a high unexplained variance (noise) in the response variable, an improvement due to a spatial neighborhood consideration (L=1) was significant ( Table4 ). An analog behavior was evident for unobserved variance levels in the range (5-35%) Table 4: Comparison of the proposed method and ordinary linear and non-linear regression when 35% unexplained variance added to the response variable and all driving attributes used for model training... ..."

Cited by 1

### Table 1: Voltage percent error in the non-linear low load zone with PID and PID-GMR

in Systems

"... In PAGE 10: ... This test has been done again, both with the PID and the PID-GMR scheme, in the linear zone of the cell characteristics and in the non-linear ones at very low and very high loads to check the improvements of the control accuracy achievable with the PID-GMR scheme. Table1 , 2, 3 show the voltage reference, the load current and the corresponding voltage percent error (difference between the reference and the real voltage) obtained with both the PID and the PID-GMR scheme respectively in the non-linear low load zone, the linear zone and the non-linear high load zone. These tables show that the PID-GMR scheme overcomes the PID one in terms of voltage error, with a resulting real voltage which better approximates the reference one.... ..."

### 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 I ADAPTATION OF THE PRE-DISTORTION PARAMETERS

### Table 1. Comparison of the amplitude of the non-linear

"... In PAGE 4: ... Also, equa- tion (17) simpli es to, jmw(a; r) = A Njmw(n) a 6 (5+n) r? : (20) So, the task of comparing the amplitude of to the N- body calibrated formula simpli es to a comparison of the normalization constants Nsc(n) and Njmw(n). The results for the cases n = 0; ?1; and ?2 are shown in Table1 . Note that, for the n = ?2 case, the agreement between our prediction and the N-body data is better than indicated in the table because, as noted by JMW, their formula underestimates the non-linear amplitude of for this spectrum.... ..."

### 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 30: The values of the power coefficients (parameters) of the non- linear model G (equation ( ) 2 ) defined by minimising W (equation ). 1

2002

"... In PAGE 67: ... For both subsystems, these values differ significantly from each other. Some architectural properties that influence the development effort for the server have no influence on the development effort for the client (these attributes are the size of the subsystem expressed in the number of classes, , and the number of subcomponents, ) and vice versa; the module strength (complexity, , that specifies the number of use cases of a component) has no influence on the development effort for the client, while it does have influence in the case of the server (Table 27 and parts of Table 29 and Table30 ). Once again, attributes, such as and , have no influence whatsoever on the development effort for both subsystems.... In PAGE 69: ... 2 a 4 2 a 4 a 2 1 1 For the server, the coefficient of attribute a gets relatively insignificant values (Table 27 and Table 29), when taking into account that the attribute has a low average value (Table 32). Once again, for the client in most cases, the corresponding value is high for both models ( Table30 and Table 31). ).... ..."