Why do these two different way to find slope give different results?

I have the following data

x = [14    18    22    26];
y = [8.5588   14.3430   21.6132   30.3740];

and I want to find the slope of this data when it is plotted on a loglog() plot. I tried two methods:

First method:

loglog(x,y);

then go to tools > basic fitting > linear fitting

the result is

y = p1*x + p2 

Coefficients:
  p1 = 1.8179
  p2 = -17.636

Norm of residuals = 
     1.4883

slope = 1.8179

Second method:

     coeffs = polyfit(log(x),log(y),1);
     slope = coeffs(1);

by this method

slope = 2.0462

Why is it so? The slope that I find by using first method is closer to the experimental results. Is there any way to do the first method through code instead of GUI?

[Luqman Saleem]

thank you for a quick response. is there anyway to access "best fitting" GUI's resutls through command line? I have a big data and can't do fitting one by one.

[Adam Danz]

Sorry, I removed my comment because it only pointed out the obvious. Check out my answer below and let me know if there are any more questions.

Answer 1

[Adam Danz]

The basic fitting tool merely calls polyfit() using your x and y values (see link for more info).

You can get the same coefficients by calling polyfit directly.

x = [14    18    22    26];
y = [8.5588   14.3430   21.6132   30.3740];
coefs = polyfit(x,y,1); 

%coefs = [1.8179      -17.636]  % Same results as using fitting tool.  

Then you can add a reference line by using refline().

hold on
rh = refline(coefs(1),coefs(2)); 
rh.Color = 'r'; 

As you'll see after plotting the reference line, it does not align with your data in log space.

[Luqman Saleem]

yes. you are right. thank you.