One possibility:
x=[0 1 2 3 4 5 6 7 8 9 10];
y=[.0242 0.1940 0.2792 0.2358 0.1386 0.0598 0.0238 0.0090 0.0034 0.0013 0.002];
objfcn = @(b,x) b(1).*x.*exp(b(2).*x);
B0 = [1; -1];
[B,rsdnrm] = fminsearch(@(b) norm(y - objfcn(b,x)), B0);
xv = linspace(min(x), max(x));
figure
plot(x, y, 'pg')
hold on
plot(xv, objfcn(B,xv), '-r')
hold off
grid
text(4.5, 0.22, sprintf('$y(x) = %.3f \\cdot x \\cdot e^{%+0.3f \\cdot x}$',B), 'Interpreter','latex')
xlabel('x')
ylabel('y(x)')
The most accurate model would be one that models the process that created your data.
This model produces:
Best Answer