Title: Discrete orthogonal polynomials in linear regression Authors:  Velimir Corovic - University of Montenegro, Faculty of mathematics and natural sciences (Montenegro) [presenting]
Abstract: The aim is to investigate the use of discrete orthogonal polynomials in estimating linear regression parameters. It is shown that the system of linear equations obtained using these polynomials is more stable than one that is obtained using a standard set of polynomials in terms of the conditional numbers generated by the norms $\|\|_1, \|\|_2$ and $\|\|_{\infty}$. These findings are also demonstrated through experiments conducted in the Matlab software package. For random samples, corresponding systems of linear equations generated are obtained by standard, and orthogonal polynomials, and their conditional numbers are compared. The results provide insights into improving the stability of linear regression parameter estimation.