Tips to narrow confidence intervals in nonlinear regression.

 Consider these tips If your confidence intervals of one or more parameters are wider than you think they should be.

Enter all the data

If you enter replicate values at each value of X (and keep the default option), Prism will fit each point individually. If you enter mean, and SD (or SEM) and n for each X value, you'll get exactly the same values.

If you calculate the means manually and only enter those mean values, Prism has less information to work with and the confidence intervals will be wider. 

If you only enter the mean and SD (or SEM) without n, Prism cannot use the SD information. It analyzes the data exactly as if you had entered only means, and the confidence intervals may be wide. 

Consider constraining a parameter to a constant value

In the Constrain tab of nonlinear regression, you can constrain any parameter to have a constant value. For example, you can constrain the bottom plateau of an exponential decay to 0, or the Hill slope of a dose response curve to 1.0 (or -1.0).

After constraining one parameter, you will often find that the confidence intervals of the other parameters are much narrower.

Consider reparameterizing the equation

This means rewriting the equation so the parameters have different meanings. One example is centering polynomial models. Another example is sigmoidal enzyme kinetics.

Another approach is to realize that you don't really want to know the value of two parameters -- what you want to know is their ratio. Rewrite the equation to fit one of those two parameters and also directly fit their ratio. You may get a narrow confidence interval that way. For example, this page explains how to fit the ratio of two EC50 values of dose-response curves.