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For a simple regression model with one or two explanatory variables,

With one explanatory variable in the model, is called a *scatter plot smoother*. SAS/INSIGHT software provides nonparametric curve estimates from smoothing spline, kernel, loess (nearest neighbors local polynomial), and fixed bandwidth local polynomial smoothers.

For smoothing spline, kernel, and fixed bandwidth local polynomial smoothers, SAS/INSIGHT software derives the smoothing parameter from a constant *c* that is independent of the units of **X**. For a loess smoother, the smoothing parameter is a positive constant .

With two explanatory variables in the model, is called a *surface smoother*. SAS/INSIGHT software provides nonparametric surface estimates from thin-plate smoothing spline and kernel smoothers. The explanatory variables are scaled by their corresponding sample interquartile ranges. The smoothing parameter is derived from a constant *c* and both are independent of the units of **X**.

Similar to parametric regression, the *R ^{2}* value for an estimate is calculated as

You can use the following methods to choose the value:

**DF**- uses the value that makes the resulting smoothing estimate have the specified degrees of freedom (
*df*).

**GCV**- uses the value that minimizes the generalized cross validation (GCV) mean squared error.

**C Value**- uses the value derived from the specified
*c*value for nonparametric smoothers other than the loess smoother.

**Alpha**- uses the specified value for the loess estimator.

If you specify a

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