## 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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