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incrmpcorr2
Compute a moving squared sample Pearson productmoment correlation coefficient incrementally.
The Pearson productmoment correlation coefficient between random variables X
and Y
is defined as
where the numerator is the covariance and the denominator is the product of the respective standard deviations.
For a sample of size W
, the sample Pearson productmoment correlation coefficient is defined as
The squared sample Pearson productmoment correlation coefficient is thus defined as the square of the sample Pearson productmoment correlation coefficient.
Installation
npm install @stdlib/statsincrmpcorr2
Usage
var incrmpcorr2 = require( '@stdlib/statsincrmpcorr2' );
incrmpcorr2( window[, mx, my] )
Returns an accumulator function
which incrementally computes a moving squared sample Pearson productmoment correlation coefficient. The window
parameter defines the number of values over which to compute the moving squared sample Pearson productmoment correlation coefficient.
var accumulator = incrmpcorr2( 3 );
If means are already known, provide mx
and my
arguments.
var accumulator = incrmpcorr2( 3, 5.0, 3.14 );
accumulator( [x, y] )
If provided input values x
and y
, the accumulator function returns an updated accumulated value. If not provided input values x
and y
, the accumulator function returns the current accumulated value.
var accumulator = incrmpcorr2( 3 );
var r2 = accumulator();
// returns null
// Fill the window...
r2 = accumulator( 2.0, 1.0 ); // [(2.0, 1.0)]
// returns 0.0
r2 = accumulator( 5.0, 3.14 ); // [(2.0, 1.0), (5.0, 3.14)]
// returns ~1.0
r2 = accumulator( 3.0, 1.0 ); // [(2.0, 1.0), (5.0, 3.14), (3.0, 1.0)]
// returns ~0.86
// Window begins sliding...
r2 = accumulator( 5.0, 9.5 ); // [(5.0, 3.14), (3.0, 1.0), (5.0, 9.5)]
// returns ~0.74
r2 = accumulator( 5.0, 1.5 ); // [(3.0, 1.0), (5.0, 9.5), (5.0, 1.5)]
// returns ~0.64
r2 = accumulator();
// returns ~0.64
Notes
 Input values are not type checked. If provided
NaN
or a value which, when used in computations, results inNaN
, the accumulated value isNaN
for at leastW1
future invocations. If nonnumeric inputs are possible, you are advised to type check and handle accordingly before passing the value to the accumulator function.  As
W
(x,y) pairs are needed to fill the window buffer, the firstW1
returned values are calculated from smaller sample sizes. Until the window is full, each returned value is calculated from all provided values.  In comparison to the sample Pearson productmoment correlation coefficient, the squared sample Pearson productmoment correlation coefficient is useful for emphasizing strong correlations.
Examples
var randu = require( '@stdlib/randombaserandu' );
var incrmpcorr2 = require( '@stdlib/statsincrmpcorr2' );
var accumulator;
var x;
var y;
var i;
// Initialize an accumulator:
accumulator = incrmpcorr2( 5 );
// For each simulated datum, update the moving squared sample correlation coefficient...
for ( i = 0; i < 100; i++ ) {
x = randu() * 100.0;
y = randu() * 100.0;
accumulator( x, y );
}
console.log( accumulator() );
See Also

@stdlib/statsincr/mapcorr
: compute a moving sample absolute Pearson productmoment correlation coefficient incrementally. 
@stdlib/statsincr/mpcorr
: compute a moving sample Pearson productmoment correlation coefficient incrementally. 
@stdlib/statsincr/pcorr2
: compute a squared sample Pearson productmoment correlation coefficient.
Notice
This package is part of 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, see the main project repository.
Community
License
See LICENSE.
Copyright
Copyright © 20162023. The Stdlib Authors.