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

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Ahmed Abdalazeez on 20 Jun 2018
Commented: Ahmed Abdalazeez on 21 Jun 2018
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

Ameer Hamza on 20 Jun 2018
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)
##### 3 CommentsShow 1 older commentHide 1 older comment
Ameer Hamza on 20 Jun 2018
solution is the estimated value of the exponent. you need to use (x,y) values from your own dataset.
Ahmed Abdalazeez on 21 Jun 2018
OK, Thank you so much

Torsten on 20 Jun 2018
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 on 21 Jun 2018
OK, thank you