README.md

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incrmpcorr2

Compute a moving squared sample Pearson product-moment correlation coefficient incrementally.

The Pearson product-moment correlation coefficient between random variables X and Y is defined as

$$\rho_{X,Y} = \frac{\mathop{\mathrm{cov}}(X,Y)}{\sigma_X \sigma_Y}$$

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 product-moment correlation coefficient is defined as

$$r = \frac{\displaystyle\sum_{i=0}^{n-1} (x_i - \bar{x})(y_i - \bar{y})}{\displaystyle\sqrt{\sum_{i=0}^{n-1} (x_i - \bar{x})^2} \displaystyle\sqrt{\displaystyle\sum_{i=0}^{n-1} (y_i - \bar{y})^2}}$$

The squared sample Pearson product-moment correlation coefficient is thus defined as the square of the sample Pearson product-moment correlation coefficient.

Usage

To use in Observable,

incrmpcorr2 = require( 'https://cdn.jsdelivr.net/gh/stdlib-js/stats-incr-mpcorr2@umd/browser.js' )

To vendor stdlib functionality and avoid installing dependency trees for Node.js, you can use the UMD server build:

var incrmpcorr2 = require( 'path/to/vendor/umd/stats-incr-mpcorr2/index.js' )

To include the bundle in a webpage,

<script type="text/javascript" src="https://cdn.jsdelivr.net/gh/stdlib-js/stats-incr-mpcorr2@umd/browser.js"></script>

If no recognized module system is present, access bundle contents via the global scope:

<script type="text/javascript">
(function () {
    window.incrmpcorr2;
})();
</script>

incrmpcorr2( window[, mx, my] )

Returns an accumulator function which incrementally computes a moving squared sample Pearson product-moment correlation coefficient. The window parameter defines the number of values over which to compute the moving squared sample Pearson product-moment 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 in NaN, the accumulated value is NaN for at least W-1 future invocations. If non-numeric 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 first W-1 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 product-moment correlation coefficient, the squared sample Pearson product-moment correlation coefficient is useful for emphasizing strong correlations.

Examples

<!DOCTYPE html>
<html lang="en">
<body>
<script type="text/javascript" src="https://cdn.jsdelivr.net/gh/stdlib-js/random-base-randu@umd/browser.js"></script>
<script type="text/javascript" src="https://cdn.jsdelivr.net/gh/stdlib-js/stats-incr-mpcorr2@umd/browser.js"></script>
<script type="text/javascript">
(function () {

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() );

})();
</script>
</body>
</html>

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See Also

• @stdlib/stats-incr/mapcorr: compute a moving sample absolute Pearson product-moment correlation coefficient incrementally.
• @stdlib/stats-incr/mpcorr: compute a moving sample Pearson product-moment correlation coefficient incrementally.
• @stdlib/stats-incr/pcorr2: compute a squared sample Pearson product-moment correlation coefficient.

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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

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License

See LICENSE.

Copyright

Copyright © 2016-2024. The Stdlib Authors.