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 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:

  • 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 \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.
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