Nonlinear Regression with Errors in X and Y
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I am dealing a series of data point X and Y, their relation is nonlinear, how can i do a nonlinear regression to obtain the fitted curve: Y=a*X^2+b*X+c? I am especially interested in the uncertainty of the quadratic coefficient: "a", i have found some programs but they only consider the error in Y without including the errors in X. Are there any way to determine the uncertainty of "a" considering errors in both X and Y?
Safwan on 22 Mar 2012
What do you mean with the errors in X. Anyway, when you plot your data you can go to Tools->Basic fitting (in the figure) and fit your data with quadratic curve. Otherwise if you have the Curve fitting Toolbox of Matlab then you can use more functions. Last suggusted option from me, you can use the fminsearch.m function of matlab to find the value of a.
Tom Lane on 23 Mar 2012
Edited: Tom Lane on 15 Dec 2017
If you just had y and one or more x variables as predictors, there is information about an errors-in-variables fit here:
If you applied this literally to your example, you'd have to imagine that x and x^2 had separate errors. There is a file exchange submission that appears to address this, but I haven't played around with it: