Is this solvable and if not, then why not?
Let's say we are given a model that looks as follows:
$y=x+ax^3+bx^5+cx^7+dx^9+\mathcal{N}(0,σ_1^2)$
Given n free choices for the input variable $x$ how can we determine which $x$'s we should choose to get the optimal approximation of the unknown coefficients $a,b,c,d$. The range for $x$ is $(0,t)$ which can of course be scaled to $(0,1)$.