Fitting data with a prescribed function

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Leon
Leon on 21 Oct 2013
Commented: Leon on 21 Oct 2013
Hello,
My question is about the fitting function. I would like to fit 5 data points to a prescribed function: A + B*x + C * log(x). The code I use is:
myfit = fittype('a + b*x + c*log(x)','dependent',{'y'},'independent',{'x'},'coefficients',{'a','b','c'});
fit1=fit(xfit,yfit,myfit)
The data points I use are:
xfit = 2.1902, 2.5940, 3.0203, 3.5356, 4.2762,
yfit = 0.5000, 1.0000, 2.0000, 4.0000, 9.0000
Now, I do get an answer, but when comparing it to the values for a,b and c I found using both Python or Wolfram Mathematica, it seems very off.
Any idea what went wrong?
The expected values are: 2.5303 + 0.0627895 x + 0.538228 Log[x]
EDIT:
clear all
close all
color='red';
xfit = [2.1902, 2.5940, 3.0203, 3.5356, 4.2762];
yfit = [0.5000, 1.0000, 2.0000, 4.0000, 9.0000];
scatter(xfit,yfit,color)
hold on
myfit = fittype('a + b*x + c*log(x)','dependent',{'y'},'independent',{'x'},'coefficients',{'a','b','c'});
fit1 = fit(xfit',yfit',myfit,'StartPoint',[2.5,0,0.5]);
plot(fit1,color)
ylim([0,10])
xlim([0,5])
This is a matlab file that should do the job. However, it still doesn't work. Adding the point [0,0] to the beginning of the list does not make any difference (it results in errors, due to log(0) = -Inf ).

Accepted Answer

Friedrich
Friedrich on 21 Oct 2013
Edited: Friedrich on 21 Oct 2013
Hi,
have you verfied the other results you are getting? What kind of LOG are you using in Python or Mathematica? In MATLAB LOG is the Natural logarithm.
When verfiying the given curve it looks very wrong:
f = @(x) 2.5303 + 0.0627895.*x + 0.538228.*log(x)
xfit = [2.1902, 2.5940, 3.0203, 3.5356, 4.2762];
yfit = [0.5000, 1.0000, 2.0000, 4.0000, 9.0000];
scatter(xfit,yfit,'red')
hold on
plot(0:0.1:5,f(0:0.1:5))
ylim([0,10])
xlim([0,5])
  4 Comments
Leon
Leon on 21 Oct 2013
I think we went wrong on the formulation, here.
In Mathematica, where I found the a, b and c value for the formula, I used the values of the Y-axis to be on the horizontal axis and the values of the X-axis to be on the vertical axis.
Could this solve our problem in matlab as well?
Leon
Leon on 21 Oct 2013
Okay, we did went wrong on the formulation of X and Y axis. When we now adjust the scatter function (scatter(yfit,xfit,'red') ), and we continue on the way we did before, we get a perfect match. Thanks for helping!

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