MATLAB: How to fit this curve

Question

x = [39.224 49.03 58.836 68.642 78.448 88.254 98.06 107.866 117.672 127.478 137.284];

y = [2.4218 3.9931 6.0817 8.7791 12.1994 16.4867 21.8260 28.4584 36.7052 47.0032 59.9637];

Answer 1

The best model is the mathematical expression of the process that created those data.

A power law fit appears to provide a reasonable approximation:

x  = [39.224 49.03 58.836 68.642 78.448 88.254 98.06 107.866 117.672 127.478 137.284];
y = [2.4218 3.9931 6.0817 8.7791 12.1994 16.4867 21.8260 28.4584 36.7052 47.0032 59.9637];
fcn = @(b,x) b(1).*x.^b(2);
B = fminsearch(@(b) norm(y - fcn(b,x)), rand(2,1));     % Power Law
figure
plot(x, y, '.')
hold on
plot(x, fcn(B,x), '-r')
hold off
grid
xlabel('X')
ylabel('Y')

producing:

.