The only way to determine the distribution of best-fit parameters is to simulate many sets of data and then look at the distribution of best-fit values following this general procedure:

1. Generate a simulated data set by adding random Gaussian error to the ideal value at each value of X.  You'll need to choose a model (equation) to simulate, the range of X values, the number of points,  and the amount of scatter.

2. Use nonlinear regression to fit a curve to the simulated data, using the same model. Record the best-fit values of the parameters.

3. Repeat steps 2-5 many (thousands) of times.

4. Construct a frequency histogram of the parameter values.

5. Repeat using a different form of the equation.

The procedure employed for generating large numbers of simulated data sets with random error is referred to as Monte Carlo analysis. Arthur Christopoulos has done this with equations commonly used in analyzing pharmacological data (Trends Pharmacol. Sci. 19:351-357, 1998), and he is a co-author of this chapter.

This procedure is explained in detail below (see How to compare parameter distributions using Prism).