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:
- 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'.
- 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.
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