Supposing I have a graph involving time (x axis time in seconds) and log of nubers of bacteria:
I would like to adjust a model given by a formula involving 5 coefficients like:
$Number = Log\left ( \frac{C_1 t}{C_2} \right ) \left ( 200\frac{C_2 C_3}{C_4C_5}\right ) $
I know the goal of nonlinear regression is to fit a model to data. So a program finds the best-fit values of the parameters in the model
So what would be the best approach to propose a multivariate regression method to adjust it And How could I know the number of iterations I would need?
I red that phases involving proposing regression model are:
Step 1. Choose a model Scientific decision that must be made by someone who understands the scientific goals of the experiment. As it is logarithmic can I split it using the fact that there are phases?
Step 2. Decide whether to constrain any parameters to constant values When performing nonlinear regression, we don't have to fit each parameter in the equation. Instead, we may fix one or more of the parameters to constant values. Like the "$C_i's$" Maybe here I could use a sigmoid or exponential? what happenes as Y axis is logaritmic?
Step 3. Choose initial values Nonlinear regression is an iterative procedure. The program must start with estimated values for each parameter. It then adjusts these initial values to improve the fit. So here I could an algorithm to perform maybe a greedy search to give some "not so bad" initial parameters?
Step 4. If fitting two or more data sets at once, decide whether to share any parameters
Step 5. Decide on a weighting scheme
Nonlinear regression programs generally weight each point equally. But there are many ways to differentially weight the points. I think using variable selection or something could help but maybe complicate things.
Step 6. Choose which results you want reported Nonlinear regression always reports the best-fit values of the parameters.
So How could i Know establish good model and how to know number of iterations needed?