123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354
import mean from "./mean.js";
/** * [Sample covariance](https://en.wikipedia.org/wiki/Sample_mean_and_covariance) of two datasets: * how much do the two datasets move together? * x and y are two datasets, represented as arrays of numbers. * * @param {Array<number>} x a sample of two or more data points * @param {Array<number>} y a sample of two or more data points * @throws {Error} if x and y do not have equal lengths * @throws {Error} if x or y have length of one or less * @returns {number} sample covariance * @example * sampleCovariance([1, 2, 3, 4, 5, 6], [6, 5, 4, 3, 2, 1]); // => -3.5 */function sampleCovariance(x, y) {    // The two datasets must have the same length which must be more than 1    if (x.length !== y.length) {        throw new Error("sampleCovariance requires samples with equal lengths");    }
    if (x.length < 2) {        throw new Error(            "sampleCovariance requires at least two data points in each sample"        );    }
    // determine the mean of each dataset so that we can judge each    // value of the dataset fairly as the difference from the mean. this    // way, if one dataset is [1, 2, 3] and [2, 3, 4], their covariance    // does not suffer because of the difference in absolute values    const xmean = mean(x);    const ymean = mean(y);    let sum = 0;
    // for each pair of values, the covariance increases when their    // difference from the mean is associated - if both are well above    // or if both are well below    // the mean, the covariance increases significantly.    for (let i = 0; i < x.length; i++) {        sum += (x[i] - xmean) * (y[i] - ymean);    }
    // this is Bessels' Correction: an adjustment made to sample statistics    // that allows for the reduced degree of freedom entailed in calculating    // values from samples rather than complete populations.    const besselsCorrection = x.length - 1;
    // the covariance is weighted by the length of the datasets.    return sum / besselsCorrection;}
export default sampleCovariance;