simple-statistics/src/r_squared.js

Simple Statistics

/**
 * The [R Squared](http://en.wikipedia.org/wiki/Coefficient_of_determination)
 * value of data compared with a function `f`
 * is the sum of the squared differences between the prediction
 * and the actual value.
 *
 * @param {Array<Array<number>>} x input data: this should be doubly-nested
 * @param {Function} func function called on `[i][0]` values within the dataset
 * @returns {number} r-squared value
 * @example
 * var samples = [[0, 0], [1, 1]];
 * var regressionLine = linearRegressionLine(linearRegression(samples));
 * rSquared(samples, regressionLine); // = 1 this line is a perfect fit
 */
function rSquared(x, func) {
    if (x.length < 2) {
        return 1;
    }

    // Compute the average y value for the actual
    // data set in order to compute the
    // _total sum of squares_
    let sum = 0;
    for (let i = 0; i < x.length; i++) {
        sum += x[i][1];
    }
    const average = sum / x.length;

    // Compute the total sum of squares - the
    // squared difference between each point
    // and the average of all points.
    let sumOfSquares = 0;
    for (let j = 0; j < x.length; j++) {
        sumOfSquares += Math.pow(average - x[j][1], 2);
    }

    // Finally estimate the error: the squared
    // difference between the estimate and the actual data
    // value at each point.
    let err = 0;
    for (let k = 0; k < x.length; k++) {
        err += Math.pow(x[k][1] - func(x[k][0]), 2);
    }

    // As the error grows larger, its ratio to the
    // sum of squares increases and the r squared
    // value grows lower.
    return 1 - err / sumOfSquares;
}

export default rSquared;