How to find a linear approximation on loglog scale?

Hello,

I have two data vectors and a loglog plot of a frequency as a function of mass, and I want to do a linear approximation on the loglog scale.

 mass=[8.55 3.08 3.24 1.23 0.418 0.155 0.035 0.122 0.133 2.23 1.69 0.89 0.61 0.437 8.5];
 frequency= [2.49 2.97 3.14 3.93 5.61 5.42 7.65 12.3 12.3 5.85 3.95 3.46 6.35 7.62 3.56];
 loglog(freq,mass,'.b');

I tried using the basic fitting tool, but I'm not getting a linear approx. on the loglog plot. Maybe polyfit could help here ? how do I do the linear approx. in the loglog scale case ?

Thanks :)

Answer 1

[Mischa Kim]

Hello Daniel, you could log your data before doing the curve fit and take it from there.

[Mischa Kim]

freq= [2.49 2.97 3.14 3.93 5.61 5.42 7.65 12.3 12.3 5.85 3.95 3.46 6.35 7.62 3.56];
mass=[8.55 3.08 3.24 1.23 0.418 0.155 0.035 0.122 0.133 2.23 1.69 0.89 0.61 0.437 8.5];
loglog(freq,mass,'.b');

lfreq = log(freq);
lmass = log(mass);

p = polyfit(lfreq, lmass, 1);
x_fitlin = linspace(0,4,2);
y_fitlin = p(1)*x_fitlin + p(2);
x_fitlog = exp(x_fitlin);
y_fitlog = exp(y_fitlin);

hold on
plot(x_fitlog,y_fitlog,'r')

Is that what you are looking for? First, log the data, then do the curve fit. In this case a polynomial of degree 1 (linear approx.). Once you have the coefficients you need to un-do the log, that's where the exp comes into play.

[Nimrod Daniel]

Indeed. Thanks !

Answer 2

[Nimrod Daniel]

Assuming I want to show the linear approx. on the loglog graph:

and not on the log of the values, how should I do it ?