# Isolate variables in nonlinear equation for regression

• I
Hi all,

I have a nonlinear equation of the form:

$$\frac{TP_x}{TP_R} = c_0 + c_1 U_R^n + c_2 \frac{T_R^2}{\sqrt{U_R}}$$

This equation describes the relationship between tidal parameters and river discharge (velocity) in tidal rivers derived from the 1-D St. Venant equations. TPx is some tidal property at station x along the river, TPR is the same tidal property at a coastal reference station, UR is the river flow (velocity), and TR is the tidal range at the reference station.

What I am trying to do is calibrate this model using contemporary data where TPx, TPR, TR, and UR are known. Therefore, I am trying to determine the coefficients (c0, c1, c2, and n) of this equation using Matlab's nlinfit function. The problem is that the last term in the equation complicates the regression because the TR variable is on the right-hand side. Is there a way separating of the independent and dependent variables for regression? Consider any combination of TPR, TPx, and TR to be the independent variable. I should also mention that 0.5 < n < 1.5.

thanks

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Thanks for the post! This is an automated courtesy bump. Sorry you aren't generating responses at the moment. Do you have any further information, come to any new conclusions or is it possible to reword the post?

Stephen Tashi
I don't use Matlab, but after some web browsing, I suggest you consider doing total least squares regression (http://www.mathworks.com/matlabcentral/fileexchange/31109-total-least-squares-method) instead of ordinary regression.

In a least square regression fit for Y = F(x1,x2,..) to data, it is assumed that x1,x2,... are measured with out "error" and that the object is to find a curve that fits noisy data for Y. So if you one of your variables ##TP_X,TP_R,T_R,U_R## is measured very precisely and free of any conceptual random variations, you could us it for Y. However, if all your variables are on an equal footing as far as measurement errors or random fluctuations go, then total least squares regression would be a better choice.

chiro