Fit A Four-Parameter Logistic Function

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Fit A Four-Parameter Logistic Function

The following NLREG program fits a 4-parameter logistic (sigmoidal) function to model heart rate as a function of blood pressure.

The five parameters that define the function are:
P1 = second plateau
P2 = range of response. Note: (P1+P2) gives the first plateau
P3 = curvature parameter
P4 = value at inflection point

Here are the NLREG statements to fit this function:

Title "Four-parameter Logistic Function (Baro4)";
Variables BP, HR;
Parameters p1=150, p2=200, p3=0.5, p4=75;
Function HR = p1+(p2/(1+exp(p3*(BP-p4))));
Plot xvar=BP, xlabel="Blood Pressure", ylabel="Heart Rate";
Data;
[ data goes here ]

Here is a plot generated by NLREG showing the Baro4 function fitted to a a set of values.