Linear Regression in Javascript [closed]

Answer 1

Simple linear regression with measures of variation ( Total sum of squares = Regression sum of squares + Error sum of squares ), Standard error of estimate SEE (Residual standard error), and coefficients of determination R2 and correlation R.

const regress = (x, y) => {
    const n = y.length;
    let sx = 0;
    let sy = 0;
    let sxy = 0;
    let sxx = 0;
    let syy = 0;
    for (let i = 0; i < n; i++) {
        sx += x[i];
        sy += y[i];
        sxy += x[i] * y[i];
        sxx += x[i] * x[i];
        syy += y[i] * y[i];
    }
    const mx = sx / n;
    const my = sy / n;
    const yy = n * syy - sy * sy;
    const xx = n * sxx - sx * sx;
    const xy = n * sxy - sx * sy;
    const slope = xy / xx;
    const intercept = my - slope * mx;
    const r = xy / Math.sqrt(xx * yy);
    const r2 = Math.pow(r,2);
    let sst = 0;
    for (let i = 0; i < n; i++) {
       sst += Math.pow((y[i] - my), 2);
    }
    const sse = sst - r2 * sst;
    const see = Math.sqrt(sse / (n - 2));
    const ssr = sst - sse;
    return {slope, intercept, r, r2, sse, ssr, sst, sy, sx, see};
}
regress([1, 2, 3, 4, 5], [1, 2, 3, 4, 3]);

Answer 2

I found this great JavaScript library.

It's very simple, and seems to work perfectly.

I also can't recommend Math.JS enough.

Answer 3

What kind of linear regression? For something simple like least squares, I'd just program it myself:

http://mathworld.wolfram.com/LeastSquaresFitting.html

The math is not too hard to follow there, give it a shot for an hour or so and let me know if it's too hard, I can try it.

EDIT:

Found someone that did it:

http://dracoblue.net/dev/linear-least-squares-in-javascript/159/

Answer 4

The simplest solution I found for the question at hand can be found in the following post: http://trentrichardson.com/2010/04/06/compute-linear-regressions-in-javascript/

Note that in addition to the linear equation, it also returns the R2 score, which can be useful.

** EDIT **

Here is the actual code snippet:

function linearRegression(y,x){
        var lr = {};
        var n = y.length;
        var sum_x = 0;
        var sum_y = 0;
        var sum_xy = 0;
        var sum_xx = 0;
        var sum_yy = 0;

        for (var i = 0; i < y.length; i++) {

            sum_x += x[i];
            sum_y += y[i];
            sum_xy += (x[i]*y[i]);
            sum_xx += (x[i]*x[i]);
            sum_yy += (y[i]*y[i]);
        } 

        lr['slope'] = (n * sum_xy - sum_x * sum_y) / (n*sum_xx - sum_x * sum_x);
        lr['intercept'] = (sum_y - lr.slope * sum_x)/n;
        lr['r2'] = Math.pow((n*sum_xy - sum_x*sum_y)/Math.sqrt((n*sum_xx-sum_x*sum_x)*(n*sum_yy-sum_y*sum_y)),2);

        return lr;
}

To use this you just need to pass it two arrays, known_y's and known_x's, so this is what you might pass:

var known_y = [1, 2, 3, 4];
var known_x = [5.2, 5.7, 5.0, 4.2];

var lr = linearRegression(known_y, known_x);
// now you have:
// lr.slope
// lr.intercept
// lr.r2

Answer 5

Here is a snippet that will take an array of triplets (x, y, r) where r is the weight of the (x, y) data point and return [a, b] such that Y = a*X + b approximate the data.

// return (a, b) that minimize
// sum_i r_i * (a*x_i+b - y_i)^2
function linear_regression( xyr )
{
    var i, 
        x, y, r,
        sumx=0, sumy=0, sumx2=0, sumy2=0, sumxy=0, sumr=0,
        a, b;

    for(i=0;i<xyr.length;i++)
    {   
        // this is our data pair
        x = xyr[i][0]; y = xyr[i][1]; 

        // this is the weight for that pair
        // set to 1 (and simplify code accordingly, ie, sumr becomes xy.length) if weighting is not needed
        r = xyr[i][2];  

        // consider checking for NaN in the x, y and r variables here 
        // (add a continue statement in that case)

        sumr += r;
        sumx += r*x;
        sumx2 += r*(x*x);
        sumy += r*y;
        sumy2 += r*(y*y);
        sumxy += r*(x*y);
    }

    // note: the denominator is the variance of the random variable X
    // the only case when it is 0 is the degenerate case X==constant
    b = (sumy*sumx2 - sumx*sumxy)/(sumr*sumx2-sumx*sumx);
    a = (sumr*sumxy - sumx*sumy)/(sumr*sumx2-sumx*sumx);

    return [a, b];
}

Answer 6

Check out https://web.archive.org/web/20150523035452/https://cgwb.nci.nih.gov/cgwbreg.html (javascript regression calculator) - pure JavaScript, not CGI calls to server. The data and processing remains on your computer. Complete R style results and R code to check the work and a visualization of the results.

See the source code for the embedded JavaScript implementations of OLS and statistics associated with the results.

The code is my effort to port the GSL library functions to JavaScript.

The codes is released under GPL because it's basically line for line porting of GPL licensed Gnu Scientific Library (GSL) code.

EDIT: Paul Lutus also provides some GPL code for regression at: http://arachnoid.com/polysolve/index.html