Question:

The logistic equation is commonly used to model growth phenomena in biological populations: Y = (L/(1+e^-a(x-b)), where Y is the response, x is the input, L, a, and b are constants. Assume that L is given as L0, find the least squares estimations of a and b.

If L0 it can be treated as a constant. So we are looking for P(a) and P(b). I was trying to write the bottom part taking the reciprocal of the negative exponential making it Y= L(1+e^a(x-b)). Then multiplying everything by the log, making Y = ln(L) (1+(ln(a))(ln(x-b)). But i don’t know if this is the right step or even what formula to apply to get Probability of a or b.