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incrpcorr2

Compute a 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 n, the sample Pearson product-moment correlation coefficient is defined as

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

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

Installation

npm install @stdlib/stats-incr-pcorr2

Alternatively,

• To load the package in a website via a script tag without installation and bundlers, use the ES Module available on the esm branch (see README).
• If you are using Deno, visit the deno branch (see README for usage intructions).
• For use in Observable, or in browser/node environments, use the Universal Module Definition (UMD) build available on the umd branch (see README).

The branches.md file summarizes the available branches and displays a diagram illustrating their relationships.

To view installation and usage instructions specific to each branch build, be sure to explicitly navigate to the respective README files on each branch, as linked to above.

Usage

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.

var accumulator = incrpcorr2();

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

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.

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

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, the squared sample Pearson product-moment correlation coefficient is useful for emphasizing strong correlations.

Examples

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() );

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See Also

• @stdlib/stats-incr/apcorr: compute a sample absolute Pearson product-moment correlation coefficient.
• @stdlib/stats-incr/mpcorr2: compute a moving squared sample Pearson product-moment correlation coefficient incrementally.
• @stdlib/stats-incr/pcorr: compute a 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.