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

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Luqman Saleem
Luqman Saleem 2019-5-20
评论： Luqman Saleem 2019-5-21
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?
  2 个评论
Luqman Saleem
Luqman Saleem 2019-5-20
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
Adam Danz 2019-5-20
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.

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采纳的回答

Adam Danz
Adam Danz 2019-5-20
编辑：Adam Danz 2019-5-21
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.

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