npm package: @stdlib/stats-incr-pcorr2
Description: Compute a squared sample Pearson product-moment correlation coefficient.
Author: The Stdlib Authors
Latest version: 0.2.3

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# incrpcorr2

[![NPM version][npm-image]][npm-url] [![Build Status][test-image]][test-url] [![Coverage Status][coverage-image]][coverage-url] <!-- [![dependencies][dependencies-image]][dependencies-url] -->

> Compute a squared sample [Pearson product-moment correlation coefficient][pearson-correlation] incrementally.

<section class="intro">

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

<!-- <equation class="equation" label="eq:pearson_correlation_coefficient" align="center" raw="\rho_{X,Y} = \frac{\operatorname{cov}(X,Y)}{\sigma_X \sigma_Y}" alt="Equation for the Pearson product-moment correlation coefficient."> -->

<div class="equation" align="center" data-raw-text="\rho_{X,Y} = \frac{\operatorname{cov}(X,Y)}{\sigma_X \sigma_Y}" data-equation="eq:pearson_correlation_coefficient">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@0086d9dadd17859fedeb3c5acc3a80d7011970e1/lib/node_modules/@stdlib/stats/incr/pcorr2/docs/img/equation_pearson_correlation_coefficient.svg" alt="Equation for the Pearson product-moment correlation coefficient.">
    <br>
</div> -->

<!-- </equation> -->

where the numerator is the [covariance][covariance] and the denominator is the product of the respective standard deviations.

For a sample of size `n`, the sample [Pearson product-moment correlation coefficient][pearson-correlation] is defined as

<!-- <equation class="equation" label="eq:sample_pearson_correlation_coefficient" align="center" raw="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} \sqrt{\sum_{i=0}^{n-1} (y_i - \bar{y})^2}}" alt="Equation for the sample Pearson product-moment correlation coefficient."> -->

<!-- <div class="equation" align="center" data-raw-text="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} \sqrt{\sum_{i=0}^{n-1} (y_i - \bar{y})^2}}" data-equation="eq:sample_pearson_correlation_coefficient">
    <img src="https://cdn.jsdelivr.net/gh/stdlib-js/stdlib@0086d9dadd17859fedeb3c5acc3a80d7011970e1/lib/node_modules/@stdlib/stats/incr/pcorr2/docs/img/equation_sample_pearson_correlation_coefficient.svg" alt="Equation for the sample Pearson product-moment correlation coefficient.">
    <br>
</div>

<!-- </equation> -->

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

</section>

<!-- /.intro -->

<section class="installation">

## Installation

```bash
npm install @stdlib/stats-incr-pcorr2
```

</section>

<section class="usage">

## Usage

```javascript
var incrpcorr2 = require( '@stdlib/stats-incr-pcorr2' );
```

#### incrpcorr2( \[mx, my] )

Returns an accumulator `function` which incrementally computes a squared sample [Pearson product-moment correlation coefficient][pearson-correlation].

```javascript
var accumulator = incrpcorr2();
```

If the means are already known, provide `mx` and `my` arguments.

```javascript
var accumulator = incrpcorr2( 3.0, -5.5 );
```

#### accumulator( \[x, y] )

If provided input value `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.

```javascript
var accumulator = incrpcorr2();

var r2 = accumulator( 2.0, 1.0 );
// returns 0.0

r2 = accumulator( 1.0, -5.0 );
// returns 1.0

r2 = accumulator( 3.0, 3.14 );
// returns ~0.93

r2 = accumulator();
// returns ~0.93
```

</section>

<!-- /.usage -->

<section class="notes">

## 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 **all** 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.
-   In comparison to the sample [Pearson product-moment correlation coefficient][pearson-correlation], the squared sample [Pearson product-moment correlation coefficient][pearson-correlation] is useful for emphasizing strong correlations.

</section>

<!-- /.notes -->

<section class="examples">

## Examples

<!-- eslint no-undef: "error" -->

```javascript
var randu = require( '@stdlib/random-base-randu' );
var incrpcorr2 = require( '@stdlib/stats-incr-pcorr2' );

var accumulator;
var x;
var y;
var i;

// Initialize an accumulator:
accumulator = incrpcorr2();

// For each simulated datum, update the squared sample correlation coefficient...
for ( i = 0; i < 100; i++ ) {
    x = randu() * 100.0;
    y = randu() * 100.0;
    accumulator( x, y );
}
console.log( accumulator() );
```

</section>

<!-- /.examples -->

<!-- Section for related `stdlib` packages. Do not manually edit this section, as it is automatically populated. -->

<section class="related">

* * *

## See Also

-   <span class="package-name">[`@stdlib/stats-incr/apcorr`][@stdlib/stats/incr/apcorr]</span><span class="delimiter">: </span><span class="description">compute a sample absolute Pearson product-moment correlation coefficient.</span>
-   <span class="package-name">[`@stdlib/stats-incr/mpcorr2`][@stdlib/stats/incr/mpcorr2]</span><span class="delimiter">: </span><span class="description">compute a moving squared sample Pearson product-moment correlation coefficient incrementally.</span>
-   <span class="package-name">[`@stdlib/stats-incr/pcorr`][@stdlib/stats/incr/pcorr]</span><span class="delimiter">: </span><span class="description">compute a sample Pearson product-moment correlation coefficient.</span>

</section>

<!-- /.related -->

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<section class="main-repo" >

* * *

## Notice

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].

#### Community

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---

## License

See [LICENSE][stdlib-license].


## Copyright

Copyright &copy; 2016-2026. The Stdlib [Authors][stdlib-authors].

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[pearson-correlation]: https://en.wikipedia.org/wiki/Pearson_correlation_coefficient

[covariance]: https://en.wikipedia.org/wiki/Covariance

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[@stdlib/stats/incr/apcorr]: https://www.npmjs.com/package/@stdlib/stats-incr-apcorr

[@stdlib/stats/incr/mpcorr2]: https://www.npmjs.com/package/@stdlib/stats-incr-mpcorr2

[@stdlib/stats/incr/pcorr]: https://www.npmjs.com/package/@stdlib/stats-incr-pcorr

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</section>

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