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Statistical Data Mining
Published in Praveen Kumar, Jay Alameda, Peter Bajcsy, Mike Folk, Momcilo Markus, Hydroinformatics: Data Integrative Approaches in Computation, Analysis, and Modeling, 2005
Amanda B. White, Praveen Kumar
Nonlinear regression (Bates and Watts, 1988) is similar to linear regression, in that a model is fit to the data and various coefficients are determined; however, the model for nonlinear regression must be specified, as it does not represent the equation of a line. Hence, the model takes the general form: y=f(X,β),
Statistics
Published in Paul L. Goethals, Natalie M. Scala, Daniel T. Bennett, Mathematics in Cyber Research, 2022
If the relationship between x and y is not linear, the regression model is called a non-linear regression model. The estimation of a non-linear regression model is often approached using the approximation method. The least-squares method can be employed to fit the non-linear regression model. However, the non-linear least squares method must be applied iteratively until the convergence is achieved. In some scenarios, it is possible to linearize the non-linear functions, such as exponential and logarithmic functions. Thus, the ordinary least squares method can be employed to estimate the unknown parameter in non-linear regression models without an iterative process.
Linear and Nonlinear Regression Models
Published in Nong Ye, Data Mining, 2013
and f is nonlinear in β. The exponential regression model given next is an example of nonlinear regression models: ()yi=β0+β1eβ2xi+εi.
Prediction of the shear strength parameters from easily-available soil properties by means of multivariate regression and artificial neural network methods
Published in Geomechanics and Geoengineering, 2022
Mojtaba Mohammadi, Seyed Mahmoud Fatemi Aghda, Mehdi Talkhablou, Akbar Cheshomi
Two methods of MNLR including logarithmic (MNLR-L) and power (MNLR-P) form were carried out on the training dataset to predict C’ and Φ’ from soil properties. In this study, three MNLR forms (mentioned in section 2.4) were used. Significant independent variables derived from the correlation coefficient have been entered into the MNLR models. Different types of models include one logarithmic form and two power forms which were developed for nonlinear regression. The MNLR-P with multiplication form (the form of Eq. 5) establish a significant relationship between C’ and soil properties (Eq. 13) with R2 = 0.87. The best MNLR relation between Φ’ and soil properties is the logarithmic form (Eq. 14) with R2 = 0.713.
Applicability of two-dimensional surface model in bacterial biosorption system: an advanced approach in bioremediation of metal ions*
Published in Environmental Technology, 2019
Equation (2) is valid for each aliquot of titrant added to the system. The model also assumes that inter- and intrachange of ions are irreversible. With these assumptions, foundation equation model equation was derived. Equation (3) shows the proposed model:where [n.Ac], Mg2+, Ca2+, H+ and OH− represent the concentration of active sites, magnesium ions, calcium ions, protons and hydroxyl ions, respectively. and show the correlation factors, which indicate the acidic and basic character of the solution. The extreme right of the equation shows the error function of the model. The accuracy of the model was evaluated through P test and F test. The goodness of fit of the model curve was studied through nonlinear regression analysis (r2), sum of square errors (SSE) and χ2 test. The relations used for SSE and χ2 test have been shown in Equations (4) and (5).where (E0)th and (E0)exp are the theoretical and experimental values of acidic and basic efflux ratios, respectively.
Evaluation of seawater intake discharge coefficient using laboratory experiments and machine learning techniques
Published in Ships and Offshore Structures, 2023
Mahmood Rahmani Firozjaei, Seyed Taghi Omid Naeeni, Hassan Akbari
Nonlinear regression is used to estimate an arbitrary nonlinear relationship between independent and dependent variables (as inputs and outputs), unlike traditional linear regression (Afrazi and Yazdani 2021). In this study, SPSS software was used to fit the multivariate regression equations for the training set. In this case, the regression coefficients were estimated using an iterative estimation algorithm based on the methods suggested and performed in NPSOL (Etemad-Shahidi and Jafari 2014). This method uses the CART algorithm for nonlinear ones to develop linear regression equations. This method was applied to develop linear regression equations from the CART algorithm to nonlinear equations (Etemad-Shahidi and Jafari 2014).