# NAME

Math::LOESS - Perl wrapper of the Locally-Weighted Regression package originally written by Cleveland, et al.

# VERSION

version 0.0001

# SYNOPSIS

```
use Math::LOESS;
my $loess = Math::LOESS->new(x => $x, y => $y);
$loess->fit();
my $fitted_values = $loess->outputs->fitted_values;
print $loess->summary();
my $prediction = $loess->predict($new_data, 1);
my $confidence_intervals = $prediction->confidence(0.05);
print $confidence_internals->{fit};
print $confidence_internals->{upper};
print $confidence_internals->{lower};
```

# CONSTRUCTION

```
new((Piddle1D|Piddle2D) :$x, Piddle1D :$y, Piddle1D :$weights=undef,
Num :$span=0.75, Str :$family='gaussian')
```

Arguments:

$x

A

`($n, $p)`

piddle for x data, where`$p`

is number of predictors. It's possible to have at most 8 predictors.$y

A

`($n, 1)`

piddle for y data.$weights

Optional

`($n, 1)`

piddle for weights to be given to individual observations. By default, an unweighted fit is carried out (all the weights are one).$span

The parameter controls the degree of smoothing. Default is 0.75.

For

`span`

< 1, the neighbourhood used for the fit includes proportion`span`

of the points, and these have tricubic weighting (proportional to`(1 - (dist/maxdist)^3)^3)`

. For`span`

> 1, all points are used, with the "maximum distance" assumed to be`span^(1/p)`

times the actual maximum distance for p explanatory variables.When provided as a construction parameter, it is like a shortcut for,

`$loess->model->span($span);`

$family

If

`"gaussian"`

fitting is by least-squares, and if`"symmetric"`

a re-descending M estimator is used with Tukey's biweight function.When provided as a construction parameter, it is like a shortcut for,

`$loess->model->family($family);`

Bad values in `$x`

, `$y`

, `$weights`

are removed.

# NAME

Math::LOESS - Perl wrapper of the Locally-Weighted Regression package originally written by Cleveland, et al.

# ATTRIBUTES

## model

Get an Math::LOESS::Model object.

## outputs

Get an Math::LOESS::Outputs object.

## x

Get input x data as a piddle.

## y

Get input y data as a piddle.

## weights

Get input weights data as a piddle.

## activated

Returns a true value if the object's `fit()`

method has been called.

# METHODS

## fit

` fit()`

## predict

` predict((Piddle1D|Piddle2D) $newdata, Bool $stderr=false)`

Returns a Math::LOESS::Prediction object.

Bad values in `$newdata`

are removed.

## summary

` summary()`

Returns a summary string. For example,

` print $loess->summary();`

# SEE ALSO

https://en.wikipedia.org/wiki/Local_regression

# AUTHOR

Stephan Loyd <sloyd@cpan.org>

# COPYRIGHT AND LICENSE

This software is copyright (c) 2019 by Stephan Loyd.

This is free software; you can redistribute it and/or modify it under the same terms as the Perl 5 programming language system itself.