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

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

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

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() );