Linear 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. Detailed information about the problem can be found in Prickett et al. (2011) Elliott et al. (2007) Prickett et al. (2010) and Jochem and Korber (1987). Data provided courtesy of Dr. RicheUe Prickett. 

Consider the problem of obtaining the values of the parameters in a theoretical equation that describes the osmotic pressure of the sodium chloride (NaCl) salt and hydroxyethyl starch (HES, chemical formula (C6Hio05) (C2H50) ). Based on the virial equation of state, it is assumed that the following equation can be used to describe the osmolality (77) of such a mixture 

Before linear regression can be applied, the above equation must be re-arranged so that all known constant information is on the left-hand side and all the unknown variables are on the right-hand side. Thus, the equation would be rewritten as 

In order to obtain the parameter estimates and analyse the results, the following MATLAB script will be used  

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