Unrepresentable Regression Parameters

In some cases, the true best-fit values for regression parameters may be too large or too small for the calculator to represent accurately. Positive numbers smaller than about $$10^{-300}$$ are rounded to $$0$$, and numbers larger than about $$10^{300}$$ are rounded to infinity which displays as undefined.

Very large or very small parameter values can occur in exponential models like $$y_1$$ ~ $$ab^{x_1}$$ or $$y_1$$ ~ $$a$$exp$$(bx_1)$$ when the $$x$$ data is far from the origin.

There are two good solutions to this problem:
1.  Measure the $$x$$ data from a baseline that is closer to the collected data. For example, for recent yearly data, measure 'years since $$2000$$' instead of 'years'.
2. Write the exponential model in a different form. Two good choices are $$y_1$$ ~ exp$$(mx_1+b)$$ or $$y_1$$ ~ $$b^{x_1-c}$$. The parameter $$c$$ in the latter model has a nice interpretation: it's the $$x$$ value for which the model predicts a $$y$$ value of 1. Both of these ways of writing exponential models are less likely to require very large or very small parameter values.