# [R] Estimating model parameters for system of equations

lstevenson louise.stevenson at lifesci.ucsb.edu
Tue Nov 15 19:03:41 CET 2011

```Hi all,

I'm trying to estimate model parameters in R for a pretty simple system of
equations, but I'm having trouble.  Here is the system of equations (all
derivatives):
eqAlgae <- (u_Amax * C_A) * (1 - (Q_Amin / Q_A))
eqQuota <- (p_max * R_V) / (K_p + R_V) - ((Q_A-Q_Amin)*u_Amax)
eqResource <- -C_A * (p_max * R_V) / (K_p + R_V)
eqSystem <- list(C_A = eqAlgae, Q_A = eqQuota, R_V = eqResource)

I want to estimate u_Amax, Q_Amin, p_max and Q_Amin with the data I've
collected using least squares. I've tried using systemfit but I'm not sure
how to write out the equations (my attempt is above but that doesn't work
since I haven't given values to the parameters I'm trying to estimate -
should I give those parameters initial values?). I've looked into the other
functions to get least squares estimates (e.g. lm() ) but I'm not sure how
to use that for a system of equations. I have some experience with R but I'm
a novice when it comes to parameter estimation, so any help would be much
appreciated! Thank you!

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```