MATLAB: Do these two different way to find slope give different results

algorithmcurve fittinglog scaleloglogmathematicsMATLAB and Simulink Student Suiteplotpolyfit

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?

Best Answer

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.
Related Question