Lotka's 3 point fit

 

  The trick for doing Lotka's 3 point fit is deriving a formula that we can solve for the unknown value of A after the other variables have been eliminated. We start by deriving formulas for B and α involving the X values. 

The expression for α is true for all values of X so we can use two data points to eliminate it resulting in one equation with one unknown.

If the data points used are evenly spaced we can eliminate Δt to get a function whose zero value gives us A. Assuming a value for A we can use Newton's method to compute the corrections dA. The convergence is fairly rapid so only a few iterations are needed to arrive at the value for A.

 One gets less known error if one assumes the fit is exact for 3 data points but that ignores any error that may be associated with these points and if the 3 point fit is used for predictions the risk is that the results will be slightly off.