x = 1:12;
y = [6.224 6.665 6.241 5.302 5.073 5.127 4.994 5.012 5.108 5.377 5.510 6.372]*10^6;
x = (x-0.5)/12;
A = [ones(12,1) cos(2*pi*x') sin(2*pi*x') cos(4*pi*x')]

A =

   1.00000000000000   0.96592582628907   0.25881904510252   0.86602540378444
   1.00000000000000   0.70710678118655   0.70710678118655   0.00000000000000
   1.00000000000000   0.25881904510252   0.96592582628907  -0.86602540378444
   1.00000000000000  -0.25881904510252   0.96592582628907  -0.86602540378444
   1.00000000000000  -0.70710678118655   0.70710678118655  -0.00000000000000
   1.00000000000000  -0.96592582628907   0.25881904510252   0.86602540378444
   1.00000000000000  -0.96592582628907  -0.25881904510252   0.86602540378444
   1.00000000000000  -0.70710678118655  -0.70710678118655   0.00000000000000
   1.00000000000000  -0.25881904510252  -0.96592582628907  -0.86602540378444
   1.00000000000000   0.25881904510252  -0.96592582628907  -0.86602540378444
   1.00000000000000   0.70710678118655  -0.70710678118655  -0.00000000000000
   1.00000000000000   0.96592582628907  -0.25881904510252   0.86602540378444

c = A\y'

c =

   1.0e+06 *

   5.58375000000000
   0.69686216653820
   0.31298484741002
   0.09944858386791

norm((A*c)'-y)

ans =

     7.547408574050438e+05

plot(x,y,x,A*c,'o')
diary off