  We exploit the idea to use the maximal-entropy method, successfully tested in
information theory and statistical thermodynamics, to determine approximating
function's coefficients and squared errors' weights simultaneously as output of
one single problem in least-square approximation. We provide evidence of the
method's capabilities and performance through its application to representative
test cases by working with polynomials as a first step. We conclude by
formulating suggestions for future work to improve the version of the method we
present in this paper.
