Statistics Toolbox

Confidence Bounds

By default, the confidence bounds are nonsimultaneous bounds for a new observation. What does this mean? Let p(x) be the true but unknown function we want to estimate. The graph contains the following three curves:

• f(x), our fitted function
• l(x), the lower confidence bounds
• u(x), the upper confidence bounds

Suppose we plan to take a new observation at the value . Call it . This new observation has its own error , so it satisfies the equation

What are the likely values for this new observation? The confidence bounds provide the answer. The interval [, ] is a 95% confidence bound for .

These are the default bounds, but the Bounds menu on the polytool figure window provides options for changing the meaning of these bounds. This menu has options that let you specify whether the bounds are to apply to the estimated function or to a new observation, and whether the bounds should be simultaneous or not. Using these options you can produce any of the following types of confidence bounds.

Simultaneous?	For Quantity	Yields Confidence Bounds for
Nonsimultaneous	Observation
Nonsimultaneous	Curve
Simultaneous	Observation	, globally for any x
Simultaneous	Curve	, simultaneously for all x

The polytool Demo

Overfitting