Implements linear regression

linear_regression.js

/* Copyright 2014 Gagarine Yaikhom (MIT License)
 *
 * Implements linear regression.
 * (see https://www.khanacademy.org for derivation)
 */
function linear_regression(datapoints) {
        var sum_x, sum_y, sum_x_2, sum_xy, mean_x, mean_y,
        m, b, n, i, d, result, se_mean, se_line;
        result = undefined;
        if (datapoints instanceof Array) {
                n = datapoints.length;
                if (n < 2)
                        throw RangeError("Not enough data points");
                sum_x = sum_y = sum_x_2 = sum_xy = 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;
                        sum_x_2 += d.x * d.x;
                        sum_xy += d.x * d.y;
                }
                mean_x = sum_x / n;
                mean_y = sum_y / n;
                d = mean_x * mean_x - sum_x_2 / n;
                if (d === 0)
                        throw EvalError("Linear regression is undefined");
                m = (mean_x * mean_y - sum_xy / n) / d;
                b = mean_y - m * mean_x;

                /* coefficient of determination: R^2 */
                se_mean = se_line = 0;
                for (i = 0; i < n; ++i) {
                        d = datapoints[i];
                        se_mean += Math.pow(mean_y - d.y, 2);
                        se_line += Math.pow(m * d.x + b - d.y, 2);
                }

                result = {
                        'm': m,
                        'b': b,
                        'R': 1 - se_line / se_mean
                };
        } else
                throw TypeError("Supplied input is not an array");
        return result;
}

function print_line(coefficients) {
        var str = "y = ";
        if (coefficients === undefined)
                throw TypeError("Supplied coefficients is undefined");
        else {
                if (coefficients.m !== 0)
                        str += coefficients.m + "x";
                if (coefficients.b !== 0) {
                        if (coefficients.m !== 0) {
                                str += (coefficients.b > 0 ? " + " : " - ");
                                str += Math.abs(coefficients.b);
                        } else
                                str += coefficients.b;
                }
                if (!isNaN(coefficients.R))
                        str += ", R^2 = " + coefficients.R;
                console.log(str);
        }
}

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': 2},
                        { 'x': 2, 'y': 1},
                        { 'x': 4, 'y': 3}
                ],
                [
                        { 'x': 1, 'y': 2},
                        { 'x': 2, 'y': 2},
                        { 'x': 4, 'y': 2}
                ],
                [
                        { '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 {
                        print_line(linear_regression(datapoints[i]));
                } catch (x) {
                        console.error(x.message);
                }
        }
}

test();