Locally-weighted polynomial regression via the LOWESS algorithm.
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> Locally-weighted polynomial regression via the LOWESS algorithm.
``bash`
npm install @stdlib/stats-lowess
`javascript`
var lowess = require( '@stdlib/stats-lowess' );
#### lowess( x, y\[, opts] )
For [input arrays][mdn-array] and/or [typed arrays][mdn-typed-array] x and y, the function returns an object holding the ordered input values x and smoothed values for y.
`javascript
var x = [
4, 4, 7, 7, 8, 9, 10, 10, 10, 11, 11, 12, 12, 12, 12, 13, 13, 13, 13, 14,
14, 14, 14, 15, 15, 15, 16, 16, 17, 17, 17, 18, 18, 18, 18, 19, 19, 19, 20,
20, 20, 20, 20, 22, 23, 24, 24, 24, 24, 25
];
var y = [
2, 10, 4, 22, 16, 10, 18, 26, 34, 17, 28, 14, 20, 24, 28, 26, 34, 34, 46,
26, 36, 60, 80, 20, 26, 54, 32, 40, 32, 40, 50, 42, 56, 76, 84, 36, 46, 68,
32, 48, 52, 56, 64, 66, 54, 70, 92, 93, 120, 85
];
var out = lowess( x, y );
/* returns
{
'x': [
4,
4,
7,
7,
...,
24,
24,
24,
25
],
'y': [
~4.857,
~4.857,
~13.1037,
~13.1037,
...,
~79.102,
~79.102,
~79.102,
~84.825
]
}
*/
`
The function accepts the following options:
- f: positive number specifying the smoothing span, i.e., the proportion of points which influence smoothing at each value. Larger values correspond to more smoothing. Default: 2/3.number
- nsteps: of iterations in the robust fit (fewer iterations translates to faster function execution). If set to zero, the nonrobust fit is returned. Default: 3.number
- delta: nonnegative which may be used to reduce the number of computations. Default: 1/100th of the range of x.boolean
- sorted: indicating if the input array x is sorted. Default: false.
By default, smoothing at each value is determined by 2/3 of all other points. To choose a different smoothing span, set the f option.
`javascript
var x = [
4, 4, 7, 7, 8, 9, 10, 10, 10, 11, 11, 12, 12, 12, 12, 13, 13, 13, 13, 14,
14, 14, 14, 15, 15, 15, 16, 16, 17, 17, 17, 18, 18, 18, 18, 19, 19, 19, 20,
20, 20, 20, 20, 22, 23, 24, 24, 24, 24, 25
];
var y = [
2, 10, 4, 22, 16, 10, 18, 26, 34, 17, 28, 14, 20, 24, 28, 26, 34, 34, 46,
26, 36, 60, 80, 20, 26, 54, 32, 40, 32, 40, 50, 42, 56, 76, 84, 36, 46, 68,
32, 48, 52, 56, 64, 66, 54, 70, 92, 93, 120, 85
];
var out = lowess( x, y, {
'f': 0.2
});
/* returns
{
'x': [
4,
4,
7,
...,
24,
24,
25
],
'y': [
~6.03,
~6.03,
~12.68,
...,
~82.575,
~82.575,
~93.028
]
}
*/
`
By default, three iterations of locally weighted regression fits are calculated after the initial fit. To set a different number of iterations for the robust fit, set the nsteps option.
`javascript
var x = [
4, 4, 7, 7, 8, 9, 10, 10, 10, 11, 11, 12, 12, 12, 12, 13, 13, 13, 13, 14,
14, 14, 14, 15, 15, 15, 16, 16, 17, 17, 17, 18, 18, 18, 18, 19, 19, 19, 20,
20, 20, 20, 20, 22, 23, 24, 24, 24, 24, 25
];
var y = [
2, 10, 4, 22, 16, 10, 18, 26, 34, 17, 28, 14, 20, 24, 28, 26, 34, 34, 46,
26, 36, 60, 80, 20, 26, 54, 32, 40, 32, 40, 50, 42, 56, 76, 84, 36, 46, 68,
32, 48, 52, 56, 64, 66, 54, 70, 92, 93, 120, 85
];
var out = lowess( x, y, {
'nsteps': 20
});
/* returns
{
'x': [
4,
...,
25
],
'y': [
~4.857,
...,
~84.825
]
}
*/
`
To save computations, set the delta option. For cases where one has a large number of (x,y)-pairs, carrying out regression calculations for all points is not likely to be necessary. By default, delta is set to 1/100th of the range of the values in x. In this case, if the values in x were uniformly scattered over the entire range, the locally weighted regression would be calculated at approximately 100 points. On the other hand, for small data sets with less than 100 observations, one can safely set the option to zero so calculations are made for each data point.
`javascript
var x = [
4, 4, 7, 7, 8, 9, 10, 10, 10, 11, 11, 12, 12, 12, 12, 13, 13, 13, 13, 14,
14, 14, 14, 15, 15, 15, 16, 16, 17, 17, 17, 18, 18, 18, 18, 19, 19, 19, 20,
20, 20, 20, 20, 22, 23, 24, 24, 24, 24, 25
];
var y = [
2, 10, 4, 22, 16, 10, 18, 26, 34, 17, 28, 14, 20, 24, 28, 26, 34, 34, 46,
26, 36, 60, 80, 20, 26, 54, 32, 40, 32, 40, 50, 42, 56, 76, 84, 36, 46, 68,
32, 48, 52, 56, 64, 66, 54, 70, 92, 93, 120, 85
];
var out = lowess( x, y, {
'delta': 0.0
});
/* returns
{
'x': [
4,
...,
25
],
'y': [
~4.857,
...,
~84.825
]
}
*/
`
If the elements of x are sorted in ascending order, set the sorted option to true.
`javascript
var x = [
4, 4, 7, 7, 8, 9, 10, 10, 10, 11, 11, 12, 12, 12, 12, 13, 13, 13, 13, 14,
14, 14, 14, 15, 15, 15, 16, 16, 17, 17, 17, 18, 18, 18, 18, 19, 19, 19, 20,
20, 20, 20, 20, 22, 23, 24, 24, 24, 24, 25
];
var y = [
2, 10, 4, 22, 16, 10, 18, 26, 34, 17, 28, 14, 20, 24, 28, 26, 34, 34, 46,
26, 36, 60, 80, 20, 26, 54, 32, 40, 32, 40, 50, 42, 56, 76, 84, 36, 46, 68,
32, 48, 52, 56, 64, 66, 54, 70, 92, 93, 120, 85
];
var out = lowess( x, y, {
'sorted': true
});
/* returns
{
'x': [
4,
...,
25
],
'y': [
~4.857,
...,
~84.825
]
}
*/
`
`javascript
var randn = require( '@stdlib/random-base-randn' );
var Float64Array = require( '@stdlib/array-float64' );
var plot = require( '@stdlib/plot-ctor' );
var lowess = require( '@stdlib/stats-lowess' );
var x;
var y;
var i;
// Create some data...
x = new Float64Array( 100 );
y = new Float64Array( x.length );
for ( i = 0; i < x.length; i++ ) {
x[ i ] = i;
y[ i ] = ( 0.5i ) + ( 10.0randn() );
}
var opts = {
'delta': 0
};
var out = lowess( x, y, opts );
var h = plot( [ x, out.x ], [ y, out.y ] );
h.lineStyle = [ 'none', '-' ];
h.symbols = [ 'closed-circle', 'none' ];
h.view( 'stdout' );
`
- Cleveland, William S. 1979. "Robust Locally and Smoothing Weighted Regression Scatterplots." _Journal of the American Statistical Association_ 74 (368): 829–36. doi:[10.1080/01621459.1979.10481038][@cleveland:1979].
- Cleveland, William S. 1981. "Lowess: A program for smoothing scatterplots by robust locally weighted regression." _American Statistician_ 35 (1): 54–55. doi:[10.2307/2683591][@cleveland:1981].
*
This package is part of [stdlib][stdlib], a standard library for JavaScript and Node.js, with an emphasis on numerical and scientific computing. The library provides a collection of robust, high performance libraries for mathematics, statistics, streams, utilities, and more.
For more information on the project, filing bug reports and feature requests, and guidance on how to develop [stdlib][stdlib], see the main project [repository][stdlib].
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---
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Copyright © 2016-2026. The Stdlib [Authors][stdlib-authors].
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[umd]: https://github.com/umdjs/umd
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[umd-url]: https://github.com/stdlib-js/stats-lowess/tree/umd
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[mdn-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Global_Objects/Array
[mdn-typed-array]: https://developer.mozilla.org/en-US/docs/Web/JavaScript/Typed_arrays
[@cleveland:1979]: https://doi.org/10.1080/01621459.1979.10481038
[@cleveland:1981]: https://doi.org/10.2307/2683591