Logistic Curve Fitting

Background for the Logistic Curve Fitting.  

    Fit the curve    to the data points  .  

Rearrange the terms  .  Then take the logarithm of both sides:  

        .  

Introduce the change of variables: .  The previous equation becomes  

             which is now "linearized."

Use this change of variables on the data points  ,  i.e. same abscissa's but transformed ordinates.

Now you have transformed data points:  .  

Use the "Fit" procedure get  Y = A X + B, which must match the form  ,  hence we must have    and  a = A.  

Remark.  For the method of "data linearization" we must know the constant  L in advance.  Since  L  is the "limiting population" for the  "S"  shaped logistic curve, a value of  L  that is appropriate to the problem at hand can usually be obtained by guessing.   

Example.  Use the method of "data linearization" to find the logistic curve that fits the data for the population of the U.S. for the years 1900-1990.  Fit the curve    to the census data for the population of the U.S.
        

Date	Populatlion
	76094000
	92407000
	106461000
	123076741
	132122446
	152271417
	180671158
	205052174
	227224681
	249464396