How to fit data to a curve with known error bars and draw it?

Using built-in functions like fit(...) or nlinfit(...), how exactly do I fit data to a curve with known error bars?

Let's say in general I have

[x,y,err_x,err_y]

And now I want to make a fit for it, say: fit=fit(x,y,'exp1')

And later want to draw everything with the errorbars using errorbar(...)

How exactly do I do that?

EDIT: knowing how to do this for the more simple case of no errors in the X axis would also help. Say I have:

[x,y,err_y]

And now I want to make a fit for it, say: fit=fit(x,y,'exp1')

[darova]

What about plot()?

f = fit();
plot(x,f(x),'r')
hold on
errorbar(x,y,err_y)
hold off

[tensorisation]

Correct me if I'm wrong but that fit won't take into account the errorbars at all, no? And what about plotting err_x as is as well?

[darova]

Yes, fit doesn't take into account errors. It approximates a function to data as close as possible.

You have the same x for errorbar and for plot. Why you need err_x?

[tensorisation]

When you have data with errors, you need a fit that takes into account the errors of your data, thats the whole point here (for example: using something like the chi^2 method, a point with a big error should contribute less than a point with a smaller error).

[darova]

What about little trick? Just to parse boundaries of data

% x, y - rows data
x1 = [x; x+0.01];
x1 = x1(:);
y1 = [y-err; y+err];
y1 = y1(:);
f = fit(x1,y1);

[darova]

Try to pass red curve instead of original one

[tensorisation]

I don't think that this produces what I'm looking for

Answer 1

[the cyclist]

Do you mean that you want to do a fit where both your x and y variables have known measurement error? (Unlike, say, an ordinary least squares fit, where all error is assumed to be in y?)

To my knowledge, MATLAB does not have a built-in function for that. I have done Deming regression using this function from the File Exchange.

[tensorisation]

Knowing how to do this for the case of only errors in y would also help me.

Let's say I have:

[x,y,err_y]

And now I want to make a fit for it, say: fit=fit(x,y,'exp1')

[Adam Danz]

related:

https://www.mathworks.com/matlabcentral/answers/447185-how-to-do-curve-fitting-on-a-data-set-with-errors-associated-to-each-data-point-y-y#answer_362893