Best Cubic Polynomial fitting

I have a data set (a versus b, see the attached file and the attached figure). I want to find the coefficients p and q of the cubic polynomial b=p*a+q*a^3 that fits the data. Please help.

Answer 1

[Torsten]

mat = [a a.^3];
rhs = b;
sol = mat\rhs;
p = sol(1)
q = sol(2)
fun=@(x) p*x + q*x.^3;
bb = fun(a);
plot(a,b,a,bb)