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I have a nonlinear equation of the form:

[tex]

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

[/tex]

This equation describes the relationship between tidal parameters and river discharge (velocity) in tidal rivers derived from the 1-D St. Venant equations. TP_{x}is some tidal property at station x along the river, TP_{R}is the same tidal property at a coastal reference station, U_{R}is the river flow (velocity), and T_{R}is the tidal range at the reference station.

What I am trying to do is calibrate this model using contemporary data where TP_{x}, TP_{R}, T_{R}, and U_{R}are known. Therefore, I am trying to determine the coefficients (c_{0}, c_{1}, c_{2}, 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 T_{R}variable is on the right-hand side. Is there a way separating of the independent and dependent variables for regression? Consider any combination of TP_{R}, TP_{x}, and T_{R}to be the independent variable. I should also mention that 0.5 < n < 1.5.

thanks

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# I Isolate variables in nonlinear equation for regression

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