fitting

x = 1:5;
y = [.5 1.7 3.4 5.7 8.4];

X = log(x);
Y = log(y);

n = length(x);

xs = 0; ys = 0; xys = 0; x2s = 0;

for i = 1:n
    xs = xs + x(i);
    ys = ys + y(i);
    x2s = x2s + x(i)^2;
    xys = xys + x(i)*y(i);
end

a1 = (n*xys - xs*ys)/(n*x2s - xs^2);
a0 = ys/n - a1*xs/n;

x_ext_log = log(1:.01:5);
y_reg_log = a0 + a1 * x_ext_log;

hold on; plot(X,Y,'o',x_ext_log,y_reg_log);

a = exp(a0);
b = a1;

x_ext = 1:.01:5;
y_reg = a*x_ext.^b;

hold on; plot(x_ext, y_reg);