cftool custom equation "worse than just fitting the mean" error

Trying to fit my stress vs. strain data, I have been using cftool in order to obtain Young's modulus as the slope of the following custom equation:

. Thus, I plugged the following equation for the function and the error goes as follows:

I checked there are no (0,0) values and of course fitting the data with a a*x+b polynomial would be conceptually wrong.

Thanks in advance.

Answer 1

[Walter Roberson]

Well, you can do a fitting to get a line with an intercept of 0, but that doesn't mean that you are going to get a good fit.

If you use a straight edge, you can construct a line between the first data point and the third-last data point (the one about 1.9e-5). If you then extend that visually to the two points on the right, you can see that the two points are above where the line would like to continue.

If you use a straight edge, you can construct a line between the third data point and the last data point. If you then extend that visually to the left, you can see that it would pass over top of the first two data points.

Basically, a straight line is not an excellent fit for that data. If you force it to fit as a straight line... then the best fit would be a line that had a negative intercept (I figure, estimating points off of the plot.) When you force a line that has an intercept of 0, you just do not get a good fit.

You have a few different possibilities:

• your data might not be accurate
• your model as a straight line might only be sufficiently accurate beyond an intitial point -- there might be an initial non-linear section
• your model as a straight line might just not be a correct model for this kind of system
• there might be confounding factors not accounted for -- for example, temperature effects, or maybe it ended up getting put together with a short length of wire of another material, or maybe the way the spring is fastened the spring has some room to move before being stretched

[Walter Roberson]

Oh, yes:

When you are using a spring system, if you stretch the spring too far you get irreversable deformation of the spring system, which would lead to nonlinear behaviour.

[Walter Roberson]

calculate

E = sigma./long;
min(E), max(E)
m = mean(E)
residue = sigma - long.*mn
plot(long, residue)

If the hypothesis that sigma = E*eta is correct then reside should be pretty close to noise, to within the accuracy of the measurements.