# Line plot on top of a log log plot

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Cameron Park on 11 Jul 2017
Commented: Cameron Park on 12 Jul 2017
I have a loglog plot of data in MATLAB and I am trying to overlay a linear fit. The linear data fitting tool doesn't work, so I was hoping to simply plot another line of slope -11/3. This line should be linear in a loglog plot, but I am having trouble plotting. Can anyone help? New to MATLAB so any advice would be useful. I have attached a picture of the plot I keep getting. The blue line is the loglog data plot, and the orange line is MATLAB's "linear fit" when using the basic plotting tool.

David Goodmanson on 11 Jul 2017
Edited: Walter Roberson on 12 Jul 2017
Hello Cameron, If you have a linear fit in the logs,
log(y) = (-11/3)log(x) + A
then exponentiate both sides:
y = x^(-11/3) exp(A)
and with C = exp(A), the fitting line (linear on loglog plot) is
y = C*x.^(-11/3)
where you just have to provide C. C could come from the same theory that gives the -(11/3), in which case you have a fit with no adjustable parameters, nice if it works. Or you could calculate C by using one (x,y) data point, or you could fit A from the first equation by taking the difference between log(y) and (-11/3)*log(x), and averaging that difference over all the values to get A. Then C = exp(A).
If you prefer log base 10, then replace log by log10 and C = exp(A) by C = 10^A everywhere.
Cameron Park on 12 Jul 2017
thank you! I used the hold on method and it worked perfectly! Appreciate the help!