Dear Ahmed Dheyab Ahmed ,

The attached chapter includes an excellent detailed answer to your question.

Best regards

Dear Issam Kaddoura

Thanks for the answer, possible example of my application on the subject

See the following two interesting papers

(1) The comparison between polynomial regression and orthogonal polynomial regression

Guo-Liang Tian

https://booksc.xyz/book/4551009/77e0a9

(2) A method of numerical solution for unsteady state problems: Inversion of Laplace transforms by recursive orthogonal polynomial regression

Kim Dong Hyun, Chang Kun Soo

https://booksc.xyz/book/2848376/cd4af5

Thanks for the answer

Where the orthogonal polynomial regression

can be applied anywhere

Some papers and a matlab implementation for regression using discrete orthogonal polynomials can be found in the work of my colleages:

https://de.mathworks.com/matlabcentral/fileexchange/41250-discrete-orthogonal-polynomial-toolbox-dopbox-version-1-8