How can I do the best fit of a power function with my original data

I have two variables (x,y). we found by eye that y = x^1/2.33, but it is not perfect for what I want and also when I test the correlation it gives me ONE but I think it should not be one because there is a variance value 0.0113. I can use the 'basic fitting' but there is no option of the power function. Thanks in advance

Answer 1

[Ameer Hamza]

You can use lsqcurvefit() for least square curve fitting. For example

% sample data
x = 0:10;
y = x.^0.33 + 0.2*rand(size(x));

f = @(x, xdata) xdata.^x(1);  % function to fit, 'x' will be estimated
solution = lsqcurvefit(f, 0, x, y)

[Ahmed Abdalazeez]

Thank you for response, I did not get you, please can you explain more, what the solution is

[Ameer Hamza]

solution is the estimated value of the exponent. you need to use (x,y) values from your own dataset.

[Ahmed Abdalazeez]

OK, Thank you so much

Answer 2

[Torsten]

xdata = ...;
ydata = ...;
a0 = 1/2.33;
fun = @(a)sum((ydata-xdata.^a).*xdata.^a.*log(xdata));
a = fzero(fun,a0)

Best wishes

Torsten.

[Ahmed Abdalazeez]

OK, thank you