scholarly journals UNIVARIATE AND MULTIVARIATE POLYNOMIAL REGRESSION CONSTRUCTION FROM A REDUNDANT REPRESENTATION USING AN ACTIVE EXPERIMENT

2020 ◽  
Vol 0 (1 (3)) ◽  
pp. 9-13
Author(s):  
Alexander Anatolievich Pavlov ◽  
Maxim Nikolaevich Holovchenko
Keyword(s):  
Polynomial Regression ◽  
Multivariate Polynomial ◽  
Active Experiment ◽  
Redundant Representation

scholarly journals ESTIMATING WITH A GIVEN ACCURACY OF THE COEFFICIENTS AT NONLINEAR TERMS OF UNIVARIATE POLYNOMIAL REGRESSION USING A SMALL NUMBER OF TESTS IN AN ARBITRARY LIMITED ACTIVE EXPERIMENT

2021 ◽  
pp. 3-7
Author(s):  
Alexander Pavlov
Keyword(s):  
Orthogonal Polynomials ◽  
Polynomial Regression ◽  
Triangular Matrix ◽  
Multivariate Polynomial ◽  
Regression Problem ◽  
Active Experiment ◽  
Scalar Variable ◽  
Univariate Polynomial ◽  
Redundant Representation ◽  
The Given

We substantiate the structure of the efficient numerical axis segment an active experiment on which allows finding estimates of the coefficients fornonlinear terms of univariate polynomial regression with high accuracy using normalized orthogonal Forsyth polynomials with a sufficiently smallnumber of experiments. For the case when an active experiment can be executed on a numerical axis segment that does not satisfy these conditions, wesubstantiate the possibility of conducting a virtual active experiment on an efficient interval of the numerical axis. According to the results of the experiment, we find estimates for nonlinear terms of the univariate polynomial regression under research as a solution of a linear equalities system withan upper non-degenerate triangular matrix of constraints. Thus, to solve the problem of estimating the coefficients for nonlinear terms of univariatepolynomial regression, it is necessary to choose an efficient interval of the numerical axis, set the minimum required number of values of the scalarvariable which belong to this segment and guarantee a given value of the variance of estimates for nonlinear terms of univariate polynomial regressionusing normalized orthogonal polynomials of Forsythe. Next, it is necessary to find with sufficient accuracy all the coefficients of the normalized orthogonal polynomials of Forsythe for the given values of the scalar variable. The resulting set of normalized orthogonal polynomials of Forsythe allows us to estimate with a given accuracy the coefficients of nonlinear terms of univariate polynomial regression in an arbitrary limited active experiment: the range of the scalar variable values can be an arbitrary segment of the numerical axis. We propose to find an estimate of the constant and ofthe coefficient at the linear term of univariate polynomial regression by solving the linear univariate regression problem using ordinary least squaresmethod in active experiment conditions. Author and his students shown in previous publications that the estimation of the coefficients for nonlinearterms of multivariate polynomial regression is reduced to the sequential construction of univariate regressions and the solution of the correspondingsystems of linear equalities. Thus, the results of the paper qualitatively increase the efficiency of finding estimates of the coefficients for nonlinearterms of multivariate polynomial regression given by a redundant representation.

scholarly journals Development of Prediction Model to Predict the Compressive Strength of Eco-Friendly Concrete Using Multivariate Polynomial Regression Combined with Stepwise Method

Materials ◽  
2022 ◽  
Vol 15 (1) ◽  
pp. 317
Author(s):  
Hamza Imran ◽  
Nadia Moneem Al-Abdaly ◽  
Mohammed Hammodi Shamsa ◽  
Amjed Shatnawi ◽  
Majed Ibrahim ◽  
...  
Keyword(s):  
Machine Learning ◽  
Compressive Strength ◽  
Prediction Model ◽  
Polynomial Regression ◽  
Learning Model ◽  
Recycled Aggregate Concrete ◽  
The Other ◽  
Multivariate Polynomial ◽  
Concrete Mixtures ◽  
Machine Learning Model

Concrete is the most widely used building material, but it is also a recognized pollutant, causing significant issues for sustainability in terms of resource depletion, energy use, and greenhouse gas emissions. As a result, efforts should be concentrated on reducing concrete’s environmental consequences in order to increase its long-term viability. In order to design environmentally friendly concrete mixtures, this research intended to create a prediction model for the compressive strength of those mixtures. The concrete mixtures that were used in this study to build our proposed prediction model are concrete mixtures that contain both recycled aggregate concrete (RAC) and ground granulated blast-furnace slag (GGBFS). A white-box machine learning model known as multivariate polynomial regression (MPR) was developed to predict the compressive strength of eco-friendly concrete. The model was compared with the other two machine learning models, where one is also a white-box machine learning model, namely linear regression (LR), and the other is the black-box machine learning model, which is a support vector machine (SVM). The newly suggested model shows robust estimation capabilities and outperforms the other two models in terms of R2 (coefficient of determination) and RMSE (root mean absolute error) measurements.

scholarly journals Design of Petroleum Physical Properties Prediction Application

2021 ◽  
Vol 1 (1) ◽  
pp. 610-619
Author(s):  
Harry Budiharjo Sulistyarso ◽  
Dyah Ayu Irawati ◽  
Joko Pamungkas ◽  
Indah Widiyaningsih
Keyword(s):  
Mathematical Model ◽  
User Interface ◽  
Physical Properties ◽  
Polynomial Regression ◽  
Regression Method ◽  
User Needs ◽  
Multivariate Polynomial ◽  
Density Data ◽  
Interface System ◽  
Made In

Based on the results of previous studies regarding the modeling of the physical properties of petroleum, a mathematical model has been built to calculate the prediction of the physical properties of petroleum. The prediction is based on viscosity, interfacial tension, and density data from the EOR laboratory in UPN Veteran Yogyakarta. The model still cannot be used independently without the Python environment, so to be used easily by more users, the model must be built into an independent application that can be installed on the user's device. In this research, the application design for the physical properties of petroleum prediction application will be carried out. The application is built using the Multivariate Polynomial Regression method according to the model to predict the physical properties of petroleum, and uses Naïve Bayes to classify the petroleum, and will be the changing result of the physical properties of petroleum modeling that has been made in a previous study. The shift from model to the application requires several adjustments, including user interface, system, and database adjustments which are implemented as the designs of application. . The design is done before the application is built to suit user needs as the result of the research.

scholarly journals Non-Linear Visualization and Importance Ratio Analysis of Multivariate Polynomial Regression Ecological Models Based on River Hydromorphology and Water Quality

Water ◽  
2021 ◽  
Vol 13 (19) ◽  
pp. 2708
Author(s):  
Vishwa Shah ◽  
Sarath Chandra K. Jagupilla ◽  
David A. Vaccari ◽  
Daniel Gebler
Keyword(s):  
Neural Networks ◽  
Water Quality ◽  
Artificial Neural Networks ◽  
Goodness Of Fit ◽  
Biological Diversity ◽  
Polynomial Regression ◽  
Ecological Status ◽  
Multivariate Polynomial ◽  
Biological Index ◽  
Artificial Neural

Multivariate polynomial regression (MPR) models were developed for five macrophyte indices. MPR models are able to capture complex interactions in the data while being tractable and transparent for further analysis. The performance of the MPR modeling approach was compared to previous work using artificial neural networks. The data were obtained from hydromorphologically modified Polish rivers with a widely varying water quality. The modeled indices were the Macrophyte Index for Rivers (MIR), the Macrophyte Biological Index for Rivers (IBMR), and the River Macrophyte Nutrient Index (RMNI). These indices measure the trophic and ecological status of the rivers. Additionally, two biological diversity indices, species richness (N) and the Simpson index (D), were modeled. The explanatory variables were physico-chemical properties depicting water quality and river hydromorphological status indices. In comparison to artificial neural networks, the MPR models performed similarly in terms of goodness of fit. However, the MPR models had advantages such as model simplicity and ability to be subject to effective visualization of complex nonlinear input–output relationships, as well as facilitating sensitivity analysis using importance ratios to identify effects of individual input variables.

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