loess
==============================================

Purpose
----------------

Computes coefficients of locally weighted regression.

Format
----------------
.. function:: { yhat, ys, xs } = loess(depvar, indvars)

    :param depvar: dependent variable.
    :type depvar: Nx1 vector

    :param indvars: independent variables.
    :type indvars: NxK matrix

    :return yhat: predicted *depvar* given *indvars*.

    :rtype yhat: Nx1 vector

    :return ys: ordinate values given abscissae values in *xs*.

    :rtype ys: *_loess_numEval*\x1 vector

    :return xs: equally spaced abscissae values.

    :rtype xs: *_loess_numEval*\x1 vector


Global Input
------------

.. csv-table::
    :widths: auto

    "*_loess_Span*", "scalar, degree of smoothing. Must be greater than 2/N. Default = .67777."
    "*_loess_NumEval*", "scalar, number of points in ys and xs. Default = 50."
    "*_loess_Degree*", "scalar, if 2, quadratic fit, otherwise linear. Default = 1."
    "*_loess_WgtType*", "scalar, type of weights. If 1, robust, symmetric weights, otherwise Gaussian. Default = 1."
    "*__output*", "scalar, if 1, iteration information and results are printed, otherwise nothing is printed."

Examples
-----------

::

      // Load dataset
      data = loadd("lowess1.dta", "h1 + depth");

      // Define independent variable
      depvar = data[., 1];

      // Defined dependent variable
      indvars = data[., 2];

      { yhat, ys, xs } = loess(depvar, indvars);


Remarks
-------

Based on Cleveland, William S. "Robust Locally Weighted Regression and
Smoothing Scatterplots." JASA, Vol. 74, 1979, 829-836.

Source
------

loess.src