Unrepresentable regression parameters

Updated August 16, 2021 14:33

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 10³⁰⁰ are rounded to infinity.

Very large or very small parameter values can occur in exponential models like $y_1 \sim ab^{x_1}$ or $y_1 \sim a\exp(bx_1)$ 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 $y_1 \sim \exp(mx_1+b)$ or $y_1 \sim b^{(x_1-c)}$ . 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.