power law fit to find exponent

I have a data in column matrix x and y

I need a power law fit say y=x^m

I require to plot scatter of y versus x and plot a power law fit on top of it ; and find m and display on graph.

any help will be appreciated!

[Star Strider]

This appears to be homework.

Post the code you have written to solve it (along with any necessary data). Describe any probllems you hare having with your code, and if it throws any error messaages, copy all the red text of those messages from your Command Window and paste them to a Comment here.

[Star Strider]

Bhowmik.U’s Answer moved here —

x=[0.1 0.2 0.3 0.4 0.5];

y=[ 0.05619065 0.79724432 1.01959856 1.03866917 1.10090886 ];

scatter(x,y);

hold on;

p=polyfit(x,y,1); m=p(1); b=exp(p(2));

ezplot(@(x) b*x.^m;[x(1) x(end)]);

hold off;

the resulting plot isnt the one I need, I need a fit such as y=x^m; where the curve mimics the scatter as close as possible.

[Star Strider]

If you want to linearise this equation:

y=x^m

take the logs of both sides. (There are much better ways to do this, however that will get you close enough.)

[Bhowmik.U]

Sir, this wasnt a "homework"...was a question my junior asked me and I wanted to help him..nuthn else.

And yes Sir. I need to find out the "m" in y=x^m; I know y and x....Linearization isnt quite my aim...I want to what power of x do y vary!

Answer 1

[Star Strider]

I would do this (no Toolboxes required):

x = linspace(0, 5, 50);                                     % Create Data
y = x.^pi + randn(size(x))*10;                              % Create Data
fcn = @(b,x) b(1).*x.^b(2) + b(3);                          % Objective Function

B = fminsearch(@(b) norm(y - fcn(b,x)), rand(3,1)*2)        % Estimate Parameters

figure
plot(x, y, '.')
hold on
plot(x, fcn(B,x), '-r')
hold off
grid

Here, ‘m’ is ‘B(2)’.

Taking the logs of both sides will only work if both ‘x’ nor ‘y’ are >=0.