Yesterday on my IT lectures I was introduced to the "Least Squares" method. Obviously it is all about finding such an $F$ that $F(x)=a_0\phi_0(x)+a_1\phi_1(x)+...+a_n\phi_n(x)$ and $R=R(a_0,a_1,...a_n)= \sum_{k=0}^{m}{[f(x_k)-y_k]^2}$ reaches its minimum.
We also asummed that our base set of functions are monomials: ($\phi_i(x)=x^{i}$) The derivation seemed pretty clear until we came across the first "overdetermined" set of equations. $\begin{cases} a+2b=6 \\[2ex] 2a-b=8 \\[2ex] 2a+3b=-4 \end{cases}$
After using the Least Squares method I got that the best approximating polynomial is $f(x)=\frac{86}{33}-\frac{52}{33}x$
My question is: how can I retrieve the given data points $(x_k, y_k)$ from the above set of equations? Any help is appreciated! :)