# 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() );
```