Nonlinear Regression Example in MATLAB

This example examines the problem of fitting a theoretical equation to experimental data in order to obtain the values of the different constants in the system. Unlike the previous case, nonlinear regression must be performed in order to obtain a result. Detailed information about the problem can be found in Ross-Rodriguez (2009). Data provided courtesy of Dr. Lisa Ross-Rodriguez. 

Consider the problem of obtaining a relationship for the ratio between the equilibrium and isotonic cell volumes given the osmotic pressure. The theoretical relationship can be written as 

In order to solve the problem in MATLAB, the function for which the parameter estimates are being obtained needs to be written as a MATLAB function. It is very important that the following points be considered when writing the function  

it must be able to deal with vector entries, that is, the dot operators should be used with times ( ) and divide (/) to give (. ) and (. /). 

Second, the header of the function must be correctly specified. The order of the inputs is parameter values, regressor values, and measured values. Each entry is assumed to be a matrix of appropriate size. The output is a single vector containing the results. Therefore, the header will be of the form 

---