Find an approximating polynomial of known degree for a given data.

Example:
For input data:

x = {0,  1,  2,  3,  4,  5,  6,   7,   8,   9,   10};
y = {1,  6,  17, 34, 57, 86, 121, 162, 209, 262, 321};

The approximating polynomial is:

3 x2 + 2 x + 1

Here, the polynomial's coefficients are (3, 2, 1).

This task is intended as a subtask for Measure relative performance of sorting algorithms implementations.

. clear
. input x y
0 1
1 6
2 17
3 34
4 57
5 86
6 121
7 162
8 209
9 262
10 321
end
 
. regress y c.x##c.x
 
      Source |       SS           df       MS      Number of obs   =        11
-------------+----------------------------------   F(2, 8)         =         .
       Model |      120362         2       60181   Prob > F        =         .
    Residual |           0         8           0   R-squared       =    1.0000
-------------+----------------------------------   Adj R-squared   =    1.0000
       Total |      120362        10     12036.2   Root MSE        =         0
 
------------------------------------------------------------------------------
           y |      Coef.   Std. Err.      t    P>|t|     [95% Conf. Interval]
-------------+----------------------------------------------------------------
           x |          2          .        .       .            .           .
             |
     c.x#c.x |          3          .        .       .            .           .
             |
       _cons |          1          .        .       .            .           .
------------------------------------------------------------------------------