Implements Pearson's product-moment correlation coefficient.

correlation_coefficient.js

/* Copyright 2014 Gagarine Yaikhom MIT License
 *
 * Implements Pearson's product-moment correlation coefficient.
 * (see http://stattrek.com/statistics/correlation.aspx?tutorial=ap)
 */
function correlation_coefficient(datapoints) {
        var sum_x, sum_y, mean_x, mean_y,
        dx, dy, sum_dx_dy, sum_dx_2, sum_dy_2,
        n, i, d, result;
        result = undefined;
        if (datapoints instanceof Array) {
                n = datapoints.length;
                if (n < 1)
                        throw RangeError("Not enough data points");

                /* calculate mean */
                sum_x = sum_y = 0;
                for (i = 0; i < n; ++i) {
                        d = datapoints[i];
                        if (typeof d.x !== "number")
                                throw TypeError("Supplied x-axis value '" + d.x
                                                + "' is not a number");
                        if (typeof d.y !== "number")
                                throw TypeError("Supplied y-axis value '" + d.y
                                                + "' is not a number");
                        sum_x += d.x;
                        sum_y += d.y;
                }
                mean_x = sum_x / n;
                mean_y = sum_y / n;

                /* calculate correlation coefficient */
                sum_dx_dy = sum_dx_2 = sum_dy_2 = 0;
                for (i = 0; i < n; ++i) {
                        d = datapoints[i];
                        dx = d.x - mean_x;
                        dy = d.y - mean_y;
                        sum_dx_dy += dx * dy;
                        sum_dx_2 += dx * dx;
                        sum_dy_2 += dy * dy;
                }
                d = Math.sqrt(sum_dx_2 * sum_dy_2);
                if (d === 0)
                        throw EvalError("Correlation coefficient is undefined");
                result = sum_dx_dy / d;
        } else
                throw TypeError("Supplied input is not an array");
        return result;
}

function test() {
        var datapoints = [
                [
                        { 'x': 1, 'y': 1},
                        { 'x': 2, 'y': 2},
                        { 'x': 3, 'y': 3},
                        { 'x': 4, 'y': 4},
                        { 'x': 5, 'y': 5},
                        { 'x': 6, 'y': 6},
                        { 'x': 7, 'y': 7},
                        { 'x': 8, 'y': 8},
                        { 'x': 9, 'y': 9},
                        { 'x':10, 'y':10}
                ],
                [
                        { 'x': 1, 'y':20},
                        { 'x': 2, 'y':18},
                        { 'x': 3, 'y':16},
                        { 'x': 4, 'y':14},
                        { 'x': 5, 'y':12},
                        { 'x': 6, 'y':10},
                        { 'x': 7, 'y': 8},
                        { 'x': 8, 'y': 6},
                        { 'x': 9, 'y': 4},
                        { 'x':10, 'y': 2}
                ],
                [
                        { 'x': 1, 'y': 3.5},
                        { 'x': 2, 'y': 5.2},
                        { 'x': 3, 'y': 4.7},
                        { 'x': 4, 'y': 8},
                        { 'x': 5, 'y':10},
                        { 'x': 6, 'y':15.25},
                        { 'x': 7, 'y':13.75},
                        { 'x': 8, 'y':12.5},
                        { 'x': 9, 'y':20.25},
                        { 'x':10, 'y':23}
                ],
                [
                        { 'x': "Apple", 'y': "Orange"},
                        { 'x': 0, 'y': 4},
                        { 'x': 0, 'y': 6},
                        { 'x': 0, 'y': 8}
                ],
                [
                        { 'x': 0, 'y': 2},
                        { 'x': 0, 'y': 4},
                        { 'x': 0, 'y': 6},
                        { 'x': 0, 'y': 8},
                        { 'x': 0, 'y':10}
                ]];

        for (var i = 0, n = datapoints.length; i < n; ++i) {
                try {
                        console.log(correlation_coefficient(datapoints[i]));
                } catch (x) {
                        console.error(x.message);
                }
        }
}

test();