Using polyfit to fit power function including the initial point x=0

I want to find the equation for data points that are given below

 x= [ 0 0.0005 0.001 0.005 0.01 0.05 0.1];

 y=[0.43 0.47 0.51 0.77 1 1.9 2.44];

Because the first x component is zero hence I could not include the first data set if I fit it as power function.

Is there a way to fit it as y=y(0) +a*x^m?

Thank you.

[Matt J]

Is m unknown? Does it have to be integer-valued?

Answer 1

[Star Strider]

You can do a power fit with fminsearch:

   x= [ 0 0.0005 0.001 0.005 0.01 0.05 0.1];
   y=[0.43 0.47 0.51 0.77 1 1.9 2.44];
   xc = linspace(min(x),max(x));

f = @(b,x) b(1).*x.^b(2);
SSE = @(b,f,x,y) sum((y-f(b,x)).^2);

B = fminsearch(@(b) SSE(b,f,x,y),  [1;1]);

figure(1)
plot(x, y, 'pr')
hold on
plot(xc, f(B,xc), '-g')
hold off
grid
legend('Data', 'Power Function Fit', 'Location', 'NW')
text(0.05, 1.2, sprintf('\\itf\\rm(\\itx\\rm) = %.1f \\itx\\rm^{%.2f}',B))

producing:

Answer 2

[the cyclist]

I assume that you mean you want to fit

y == y0 + a * x^m

and you want to estimate values for y0, a, and m.

If you have the Statistics Toolbox, you can use the nlinfit function to do that sort of fit.

Answer 3

[Chad Greene]

x=[0 0.0005 0.001 0.005 0.01 0.05 0.1];
y=[0.43 0.47 0.51 0.77 1 1.9 2.44];

plot(x,y,'ko')
hold on

linearFit = polyfit(x,y,1); 
xfit = linspace(0,.1,100);
yfitLinear = linearFit(1)*xfit + linearFit(2); 
plot(xfit,yfitLinear,'b')

secondOrderFit = polyfit(x,y,2); 
yfitSecondOrder = secondOrderFit(1)*xfit.^2 + secondOrderFit(2)*xfit + secondOrderFit(3); 
plot(xfit,yfitSecondOrder,'r')

legend('original data','linear fit','second order fit','location','southeast')
legend boxoff
box off

You could do whatever power of fit you'd like.

[the cyclist]

This might be useful, but it is not a power law fit, which is what I think Laura is asking for.