Hello !

I have come up with :

a*P0(x) + b*P1(x) + c*P2(x) where a=1.175201 ; b=1.103638 ; c=0.357814

P0(x), P1(x), P2(x) are Legendre polynomials.

This result is the same as :

A + B*x + C*x² where A=0.996294 ; B= 1.103638 ; C=0.536722

Classical polynomial regression leads exactly to the same result.

In order to find where is the mistake in your calculus, you should show the details of what you did.