## Parametric Curves: Confidence Curves

You can add two types of confidence
curves for the predicted values.
One curve is for the mean value of the response,
and the other is for the prediction of a new observation.
For the *i*th observation, a confidence interval
that covers the expected value of the response with
probability has upper and lower limits

where is the critical value
of the Student's *t* statistic with degrees of freedom
equal to the degrees of freedom for the mean squared error
and *h*_{i} is the *i*th diagonal
element of the hat matrix **H**.
The hat matrix **H** is described in the section
"Output Variables" later in this chapter.
The upper and
lower limits for prediction are

You can generate confidence curves for a parametric
regression fit by choosing the confidence coefficient
from the **Curves:Confidence Curves** menu.

**Figure 39.38:** Confidence Curves Menu

Figure 39.39 displays a quadratic polynomial
fit with 95% mean confidence curves for the response.
Use the **Coefficient** slider to
change the confidence coefficient.

**Figure 39.39:** A Quadratic Polynomial Fit with
99% Mean Confidence Curves

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