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# incrmrss

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

<section class="intro">

For a window of size `W`, 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}^{W-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}^{W-1} (y_i - x_i)^2" data-equation="eq:residual_sum_of_squares">
    <img src="https://cdn.rawgit.com/stdlib-js/stdlib/df44d1456cc422c38a368a47b586b7eaffb19cc8/lib/node_modules/@stdlib/stats/incr/mrss/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 incrmrss = require( '@stdlib/stats/incr/mrss' );
```

#### incrmrss( window )

Returns an accumulator `function` which incrementally computes a moving [residual sum of squares][residual-sum-of-squares]. The `window` parameter defines the number of values over which to compute the moving [residual sum of squares][residual-sum-of-squares].

```javascript
var accumulator = incrmrss( 3 );
```

#### 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 = incrmrss( 3 );

var r = accumulator();
// returns null

// Fill the window...
r = accumulator( 2.0, 3.0 ); // [(2.0,3.0)]
// returns 1.0

r = accumulator( -1.0, 4.0 ); // [(2.0,3.0), (-1.0,4.0)]
// returns 26.0

r = accumulator( 3.0, 9.0 ); // [(2.0,3.0), (-1.0,4.0), (3.0,9.0)]
// returns 62.0

// Window begins sliding...
r = accumulator( -7.0, 3.0 ); // [(-1.0,4.0), (3.0,9.0), (-7.0,3.0)]
// returns 161.0

r = accumulator( -5.0, -3.0 ); // [(3.0,9.0), (-7.0,3.0), (-5.0,-3.0)]
// returns 140.0

r = accumulator();
// returns 140.0
```

</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 **at least** `W-1` 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.
-   As `W` (x,y) pairs are needed to fill the window buffer, the first `W-1` returned values are calculated from smaller sample sizes. Until the window is full, each returned value is calculated from all provided values.

</section>

<!-- /.notes -->

<section class="examples">

## Examples

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

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

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

// Initialize an accumulator:
accumulator = incrmrss( 5 );

// For each simulated datum, update the moving 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 -->
