Abstract
An automated coefficients calculation of the regression model based on the experimental data in the form of a planning matrix is considered. The calculations are based on polynomial regression with possible consideration of the interaction effects between its factors. The application of the Moore – Penrose pseudoinverse matrix for determining the regression equation coefficients is shown. The choice of the calculated planning matrix is carried out taking into account the determination coefficient value and the factors’ calculated matrix rank. Calculation verification is carried out using the rank correlation between the experimental and calculated response functions. The experimental part of the work is given to determine the dependence of fungal resistance and fungicidal properties of filled cement composites on the type and grain size composition of the filler.
Highlights
Cement composites are widely studied in order to determine both the most preferable composition and to analyze their properties under various operating conditions [1,2,3]
To obtain a calculated adequate regression model, interaction effects can be introduced into the planning matrix, and various existing regression methods can be applied
It is assumed that the rank of the matrix X is equal to the dimension of the response function Y, i.e.,the rank (X) = n
Summary
Cement composites are widely studied in order to determine both the most preferable composition and to analyze their properties under various operating conditions [1,2,3]. The problem of determining a regression model that reflects the investigated relationships between the properties of composite materials is posed and solved [7,8,9]. To check the adequacy of the results obtained, such an indicator as the determination coefficient R2can be used [12], which gives an opportunity to compare the values’ closeness of the experimental and calculated response functions. Experimental data analysis can be performed using regression analysis methods and experiment planning. To obtain a calculated adequate regression model, interaction effects can be introduced into the planning matrix, and various existing regression methods can be applied. This paper highlights the results ofa computational planning matrix formation using polynomial regression, which lays down in its implementation the principle of expanding. It can be noted that in modern programming environments such as Python there are modules / classes to implement polynomial regression
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