Confidence and prediction bands

Distinguishing confidence from prediction bands

Prism can superimpose on your graph either confidence or prediction bands for the regression curve. Choose in the Diagnostics tab of the Nonlinear regression parameters dialog. Learn how they are calculated.

The 95% confidence bands enclose the area that you can be 95% sure contains the true curve. It gives you a visual sense of how well your data define the best-fit curve.

The 95% prediction bands enclose the area that you expect to enclose 95% of future data points. This includes both the uncertainty in the true position of the curve (enclosed by the confidence bands), and also accounts for scatter of data around the curve. Therefore, prediction bands are always wider than confidence bands. When you have lots of data points, the discrepancy is huge.

With each nonlinear fit, Prism can plot either the confidence bands or the prediction bands, but not both. To plot both on one graph, fit the curve twice and superimpose both fits on the same graph.

When to plot confidence and prediction bands

Confidence bands let you see how well your data define the curve. The confidence intervals for the parameters define the precision of the fit. The confidence bands sort of combine these in a visual way. Use confidence bands to learn how well your data define the best-fit curve.

Prediction bands are wider, to also include the scatter of the data. Use prediction bands when your main goal is interpolation from a standard curve.

Fine-tuning the appearance of the confidence and prediction bands

If you check the option on the Fit tab, Prism will automatically superimpose the confidence or prediction band on the graph.

To adjust the appearance of the confidence or prediction bands, go to the Format Graph dialog, select the dataset that represents the best fit curve, and adjust the error bars and area fill settings. You can also choose to fill the area enclosed by the confidence or prediction bands.

How to see the confidence or prediction bands numerically

If you want to see the confidence or prediction bands as numbers, first go to the Range tab and check the option to create a table of XY values. Then view the "Curve" results page. At each X value, it shows you the Y value of the curve, as well as plus and minus error values that define the prediction or confidence band.