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Fit Analyses |

If the form of the regression function *f* is
known except for certain parameters, the model
is called a *parametric regression model*.
Furthermore, if the regression function is linear in the
unknown parameters, the model is called a *linear model*.
In the case of linear models with the error term
assumed to be
normally distributed, you can use classical linear
models to explore the relationship between the
response variable and the explanatory variables.
A *nonparametric model* generally assumes
only that *f* belongs to some infinite-
dimensional collection of functions.
For example, *f* may be assumed to be differentiable
with a square-integrable second derivative.
When there is only one explanatory X variable,
you can use nonparametric smoothing methods,
such as smoothing splines, kernel estimators,
and local polynomial smoothers.
You can also request confidence ellipses and parametric
fits (mean, linear regression, and polynomial curves)
with a linear model.
These are added to a scatter plot generated from **Y** by a
single **X** and are described in the "Fit Curves" section.
When there are two explanatory variables in the model,
you can create parametric and nonparametric
(kernel and thin-plate smoothing spline) response surface plots.
With more than two explanatory variables in the model,
a parametric profile response surface plot with
two selected explanatory variables can be created.

When the response *y*_{i} has a distribution
from the exponential family (normal, inverse Gaussian, gamma,
Poisson, binomial), and the mean of
the response variable *y*_{i} is assumed to be
related to a linear predictor through a monotone function *g*

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