Line plot on top of a log log plot

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.

Answer 1

[David Goodmanson]

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]

Thank you for your response, that definitely helped with creating the line, however I am still having problems plotting them on the same graph. When I plot this line, it erases the last plot of all the data. Any thoughts on how to plot both at once?

[Walter Roberson]

hold on

?

[David Goodmanson]

You could do independent plot commands with 'hold on' active like Walter has mentioned, or you could do

y1 = C*x.^(-11/3);
loglog(x,y,x,y1)      [corrected per Walter's comment]

[Walter Roberson]

Well, loglog(x,y,x,y1)

[David Goodmanson]

yes.

[Cameron Park]

thank you! I used the hold on method and it worked perfectly! Appreciate the help!