wink-statistics
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Fast and Numerically Stable Statistical Analysis Utilities
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JavaScript
// wink-statistics
// Fast and Numerically Stable Statistical Analysis Utilities.
//
// Copyright (C) GRAYPE Systems Private Limited
//
// This file is part of “wink-statistics”.
//
// Permission is hereby granted, free of charge, to any person obtaining a
// copy of this software and associated documentation files (the "Software"),
// to deal in the Software without restriction, including without limitation
// the rights to use, copy, modify, merge, publish, distribute, sublicense,
// and/or sell copies of the Software, and to permit persons to whom the
// Software is furnished to do so, subject to the following conditions:
//
// The above copyright notice and this permission notice shall be included
// in all copies or substantial portions of the Software.
//
// THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS
// OR IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
// FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL
// THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
// LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING
// FROM, OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER
// DEALINGS IN THE SOFTWARE.
// ## streaming
var getValidFD = require( './get-valid-fd.js' );
// ### slr (Simple Linear Regression)
/**
*
* Linear Regression is determined incrementally with arrival of each pair of `x`
* and `y` values from the data stream.
*
* The [`compute()`](https://winkjs.org/wink-statistics/Stream.html#compute) requires
* two numeric arguments viz. `x` — independant variable and `y` — dependant variable.
*
* The [`result()`](https://winkjs.org/wink-statistics/Stream.html#result) returns
* an object containing `slope`, `intercept`, `r`, `r2`, `se` along with
* the `size` of data i.e. number of x & y pairs. It has an alias
* [`value()`](https://winkjs.org/wink-statistics/Stream.html#value).
*
* *In case of any error such as no
* input data or zero variance, correlation object will be an empty one*.
*
* @memberof streaming#
* @return {Stream} Object containing methods such as `compute()`, `result()` & `reset()`.
* @example
* var regression = simpleLinearRegression();
* regression.compute( 10, 80 );
* regression.compute( 15, 75 );
* regression.compute( 16, 65 );
* regression.compute( 18, 50 );
* regression.compute( 21, 45 );
* regression.compute( 30, 30 );
* regression.compute( 36, 18 );
* regression.compute( 40, 9 );
* regression.result();
* // returns { slope: -2.3621,
* // intercept: 101.4188,
* // r: -0.9766,
* // r2: 0.9537,
* // se: 5.624,
* // size: 8
* // }
*/
var simpleLinearRegression = function () {
var meanX = 0;
var meanY = 0;
var varX = 0;
var varY = 0;
var covXY = 0;
var items = 0;
// Returned!
var methods = Object.create( null );
methods.compute = function ( xi, yi ) {
var dx, dy;
items += 1;
dx = xi - meanX;
dy = yi - meanY;
meanX += dx / items;
meanY += dy / items;
covXY += dx * ( yi - meanY );
varX += dx * ( xi - meanX );
varY += dy * ( yi - meanY );
return undefined;
}; // compute()
methods.result = function ( fractionDigits ) {
var model = Object.create( null );
var fd = getValidFD( fractionDigits );
if ( ( items > 1 ) && ( varX !== 0 ) && ( varY !== 0 ) ) {
model.slope = +( covXY / varX ).toFixed( fd );
model.intercept = +( meanY - ( model.slope * meanX ) ).toFixed( fd );
model.r = +( covXY / Math.sqrt( varX * varY ) ).toFixed( fd );
model.r2 = +( model.r * model.r ).toFixed( fd );
model.se = +( Math.sqrt( varY / ( items - 1 ) ) * Math.sqrt( 1 - model.r2 ) ).toFixed( fd );
model.size = items;
}
return model;
}; // result()
methods.reset = function () {
meanX = 0;
meanY = 0;
varX = 0;
varY = 0;
covXY = 0;
items = 0;
}; // reset()
// There is no single correlation value; create an alias!
methods.value = methods.result;
return methods;
}; // simpleLinearRegression()
module.exports = simpleLinearRegression;