\section{Problem}
Given following samples:
\begin{center}
  \begin{tabular}{| c | c |}
\hline
$x_i$ & $y_i$ \\
\hline
-5 & -6.5743\\
\hline
-4 & 0.9765\\
\hline
-3 & 3.1026\\
\hline
-2 & 1.8572 \\
\hline
-1 & 1.3165 \\
\hline
0 & -0.6144 \\
\hline
1 & 0.1032 \\
\hline
2 & 0.3729 \\
\hline
3 & 2.5327 \\
\hline
4 & 7.3857 \\
\hline
5 & 9.4892 \\
\hline

\end{tabular}
\end{center}

We have to determine polynomial function $ y  = f(x) $ that best fits this data. \\
We will use least-square approximation using system of normal equation with QR factorization.