I have a table of values that are supposed to be used as points for exponential regression (least squares method).
Values in both columns are uncertain, which means that the function itself is a little uncertain as well. The rule is:
$$real\ value = measured\ value \pm uncertainty$$
But how ...
Is this a kind of diode you're measuring the current and tension? I'm just asking out of curiosity :) Tell me if understood correctly, you want to have three curves on your graphic, the two others being the ones relatively to the addition and substraction of the uncertainty?
Yes, I want to combine the values so that I get the most deviant exponentials that are deemed possible. And you're right, here is the complete task. It's giving me a hard time.
:D , I've been there too. My school is called "école supérieure d'électricité " = " superior school of electricity", I've suffered as well on this. How do you evaluate the uncertainty? Because for a start I'd substract it to each of your measures, ask for an exponential regression on the shifted values. Now it depends how the exponential regression is implemented. Is it automatic or do you have to plot th log of your values and get a straight line?
Ok I've read your post of physics.stackexchange, I think you got what you wanted essentially. $ \alpha$ is your coefficient $\frac{e}{kT}$, so you can get your boltzmann constant (k). Do that for each of your curves (measured, -uncertainty, +uncertainty), you will get three values of k from which you will get the uncertainty on k. Is it what you were looking for?
That't the problem - is -uncertainty really the most extreme deviation from measured when the function is plotted? If you look on the graph, the red is almost the same as green - the deviation is quite asymmetric. If I had more time, I could probably let Matlab plot all the combinations of +-uncertainty to find the most deviated functions.
Would you help me in chat?
If we figure out the solutions, you can post it as an answer...
Ok so the question is: can we find a certain order of addition and substraction of uncertainty ( substract uncertainty to the first measure, add it to the next, and the following one, then substract to the fourth measure, etc... for instace) such as the deviation from the regression did on the untouched measures is the largest possible? And is it: always substract uncertainty, or always add it?
Ok, I'd rather use a linear regression with the ln of the relation existing between I and U :
ln(I/A) = b*U (alpha is too long to write) Question is: how to minimize or maximize the coefficient b? That's what'll give you your most deviated functions. Then I think what is the most deviated way of injecting uncertainty is: you want to maximize b => maximize I and minimize U : +A , -V you want minimize b => minimize I and maximize U : -A , +V What do you think?
Maybe it's a bit naive, I could try to refine it with optimization methods but i don"t have my course with me and don't remember all of it very well.
The orange deviation is the +A -V http://fooplot.com/#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…
It's not extreme, since it has intersections with other plots
I'm trying this on regular linear relations: you draw little squares around each point (that's your two dimensional uncertainty) and you can tell visually that when you choose the upper left side of the square you get the most positively deviated regression
That's something else, like other constants in your equation you only evaluate one parameter at the time - An unknown error has occurred
forget the end of my post, I had an error while posting it
you could look for a measure of the residual current when U is very small
that'll give Io, since the exponential will be assimilated to 1 if you combine things correctly when taking into account the actual values of e, k , and T( assume 20° celsius, sorry I'm french :) )
Now when you have a good value of Io, you can settle it and start studying k, if you know the value of e, and the temperature
it's just that when you want to to evaluate a parameter in an equation that contains several, you need to settle all other parameters, or else you won't get anything straight
Discussion between Tomáš Zato and mvggz
Discussion between Tomáš Zato and mvggz