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# incrrss

> Compute the [residual sum of squares][residual-sum-of-squares] (RSS) incrementally.

<section class="intro">

The [**residual sum of squares**][residual-sum-of-squares] (also referred to as the **sum of squared residuals** (SSR) and the **sum of squared errors** (SSE)) is defined as

<!-- <equation class="equation" label="eq:residual_sum_of_squares" align="center" raw="\operatorname{RSS} = \sum_{i=0}^{n-1} (y_i - x_i)^2" alt="Equation for the residual sum of squares."> -->

<div class="equation" align="center" data-raw-text="\operatorname{RSS} = \sum_{i=0}^{n-1} (y_i - x_i)^2" data-equation="eq:residual_sum_of_squares">
    <img src="https://cdn.rawgit.com/stdlib-js/stdlib/78799028a150a44d463029bdb62ac870b1c1f9d4/lib/node_modules/@stdlib/stats/incr/rss/docs/img/equation_residual_sum_of_squares.svg" alt="Equation for the residual sum of squares.">
    <br>
</div>

<!-- </equation> -->

</section>

<!-- /.intro -->

<section class="usage">

## Usage

```javascript
var incrrss = require( '@stdlib/stats/incr/rss' );
```

#### incrrss()

Returns an accumulator `function` which incrementally computes the [residual sum of squares][residual-sum-of-squares].

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

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

If provided input values `x` and `y`, the accumulator function returns an updated [residual sum of squares][residual-sum-of-squares]. If not provided input values `x` and `y`, the accumulator function returns the current [residual sum of squares][residual-sum-of-squares].

```javascript
var accumulator = incrrss();

var r = accumulator( 2.0, 3.0 );
// returns 1.0

r = accumulator( -1.0, -4.0 );
// returns 10.0

r = accumulator( -3.0, 5.0 );
// returns 74.0

r = accumulator();
// returns 74.0
```

</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.

</section>

<!-- /.notes -->

<section class="examples">

## Examples

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

```javascript
var randu = require( '@stdlib/random/base/randu' );
var incrrss = require( '@stdlib/stats/incr/rss' );

var accumulator;
var v1;
var v2;
var i;

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

// For each simulated datum, update the residual sum of squares...
for ( i = 0; i < 100; i++ ) {
    v1 = ( randu()*100.0 ) - 50.0;
    v2 = ( randu()*100.0 ) - 50.0;
    accumulator( v1, v2 );
}
console.log( accumulator() );
```

</section>

<!-- /.examples -->

<section class="links">

[residual-sum-of-squares]: https://en.wikipedia.org/wiki/Residual_sum_of_squares

</section>

<!-- /.links -->
