Nonlinear Regression with Errors in X and Y

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harry wang
harry wang 2012-3-22
编辑： Tom Lane 2017-12-15
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?
Mike

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回答（3 个）

Safwan
Safwan 2012-3-22
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.
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harry wang
harry wang 2012-3-22
I can find out the value of a using what you suggested, but how to determine the uncertainty of "a"? if i know the errors range for X and Y.

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Sean de Wolski
Sean de Wolski 2012-3-22
That looks like a multiple linear regression to me.
doc polyfit
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Safwan
Safwan 2012-3-22
Hi Sean, i have a question for you. Have you ever tried to convert a polyfit block (Simulink) into C code by the embedded coder?

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Tom Lane
Tom Lane 2012-3-23
编辑：Tom Lane 2017-12-15
If you just had y and one or more x variables as predictors, there is information about an errors-in-variables fit here:
https://www.mathworks.com/help/stats/examples/fitting-an-orthogonal-regression-using-principal-components-analysis.html
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:
http://www.mathworks.com/matlabcentral/fileexchange/31109
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harry wang
harry wang 2012-3-23
I have checked out this program on total least square method, it seems it can only determine the error for the sum of squared orthogonal distance, it could not determine the errors for "a", "b", and "c".

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