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 Comparative Measurements of Local Seismic Rotations by Three Independent Methods

Sensors ◽  
2020 ◽  
Vol 20 (19) ◽  
pp. 5679
Author(s):  
Johana Brokešová ◽  
Jiří Málek
Keyword(s):  
Seismic Source ◽  
Medium Size ◽  
Period Range ◽  
Small Aperture ◽  
Technical Problems ◽  
Rotation Rates ◽  
Active Experiment ◽  
Short Period ◽  
Order Of Magnitude ◽  
The Given

A comparative active experiment that is aimed at collocated measurement of seismic rotation rates along three orthogonal axes by means of three different methods is described. The rotation rates in a short-period range of 6–20 Hz were obtained using three different methods: the 6C Rotaphone sensor system developed by the authors, the commercial R-1 rotational sensor by Eentec, and a small-aperture array of twelve standard velocigraphs in a rectangular arrangement. Those three methods are compared and discussed in detail. A medium-size quarry blast was used as a seismic source. At a distance of approximately 240 m, the rotation rates reached an amplitude of the order of magnitude of 10−4–10−5 rad/s. The array derived rotation rates displayed serious limitations, as clearly documented. The R-1 instruments have shown certain technical problems that partly limit their applicability. The measured rotation rates were compared to the relevant acceleration components according to rotation-to-translation relations. Out of all the three methods, the records best matching the acceleration components were made by Rotaphone. The experiment also revealed that rotation rates in the given short-period range noticeably changed over a distance as short as 2 m.

Time Series Analysis of New Cars Sale in Bosnia and Herzegovina

2015 ◽  
Vol 806 ◽  
pp. 287-293
Author(s):  
Esad Jakupović ◽  
Vladimir Stojanović ◽  
Sanel Jakupović ◽  
Dragana Trnavac
Keyword(s):  
Time Series ◽  
Bosnia And Herzegovina ◽  
Polynomial Regression ◽  
Growth Index ◽  
Coefficient Of Determination ◽  
Chain Growth ◽  
Degree Polynomial ◽  
Car Sales ◽  
The Given ◽  
Polynomial Regression Model

The paper provides analysis of new car sales in Bosnia and Herzegovina for the period 2007-2014. For the examined period new car sales in B&H was reduced by 53.67%, from 12449 in 2007 to 6682 in 2014. The trend can be approximated using 3rd degree polynomial regression model with coefficient of determination R2=0,845. Most new cars sold were by Skoda and least was sold by Porsche. Total number of sold vehicles for this period was 73152. We also present annual growth, chain growth and cumulative growth index for the given period.

A direct method of beam-height correction in small-angle X-ray scattering

1993 ◽  
Vol 26 (6) ◽  
pp. 787-794 ◽  
Author(s):  
M. A. Singh ◽  
S. S. Ghosh ◽  
R. F. Shannon
Keyword(s):  
Small Angle ◽  
Direct Method ◽  
Triangular Matrix ◽  
Random Errors ◽  
X Ray ◽  
X Ray Scattering ◽  
Beam Height ◽  
The Given ◽  
A Direct Method ◽  
Ray Scattering

A direct (i.e. noniterative) method for desmearing the beam-height effect in small-angle X-ray scattering is discussed. The method is applicable to rectangular collimation systems with arbitrary beam-height intensity profiles. The process involves the construction of an upper-triangular matrix of terms containing the resolution information. A straightforward back-substitution process can then be used to determine the ideal pinhole-collimated curve for any experimental curve obtained with the given resolution. The principal advantage of the method lies in its simplicity, which facilitates an examination of the propagation of random errors through the desmearing process. A comparison between the direct method and the iterative approach of Glatter [J. Appl. Cryst. (1974), 7, 147–153] is made to illustrate the efficiency of the technique.

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.

Sign in / Sign up

Export Citation Format

Share Document