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    Fit A Five-Parameter Logistic Function

    In their paper "A five-parameter logistic equation for investigating asymmetry of curvature in baroreflex studies," James H. Ricketts and Geoffrey A. Head develop a 5-parameter logistic (sigmoidal) function to model heart rate as a function of blood pressure. They call this model "Baro5".

    The five parameters that define the function are:
    P1 = asymptotic minimum
    P2 = asymptotic maximum
    P3 = slope parameter
    P4 = value at inflection point
    p5 = slope parameter

    Here are the NLREG statements to fit this function:

    Title "Five-parameter Logistic Function (Baro5)";
    Variables BP, HR;
    Parameters p1=50, p2=200, p3=-0.5, p4=85, p5=-0.5;
    Double c, f, g, h;
    c = 2*p3*p5/abs(p3+p5);
    f = 1/(1+exp(-c*(p4-BP)));
    g = exp(p3*(p4-BP));
    h = exp(p5*(p4-BP));
    Function HR = p1+(p2/(1+f*g+(1-f)*h));
    Plot xvar=BP, xlabel="Blood Pressure", ylabel="Heart Rate";
    [ data goes here ]

    Here is a plot generated by NLREG showing the Baro5 function fitted to a a set of values.

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