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.

use Clifford;
 
constant @x1 = <0 1 2 3 4 5 6 7 8 9 10>;
constant @y = <1 6 17 34 57 86 121 162 209 262 321>;
 
constant $x0 = [+] @e[^@x1];
constant $x1 = [+] @x1 Z* @e;
constant $x2 = [+] @x1 »**» 2  Z* @e;
 
constant $y  = [+] @y Z* @e;
 
my $J = $x1 ∧ $x2;
my $I = $x0 ∧ $J;
 
my $I2 = ($I·$I.reversion).Real;
 
.say for
(($y ∧ $J)·$I.reversion)/$I2,
(($y ∧ ($x2 ∧ $x0))·$I.reversion)/$I2,
(($y ∧ ($x0 ∧ $x1))·$I.reversion)/$I2;