slopeとinterceptをcovarianceとvarianceから求められるか実践

line-regression.test.ts

import { variance } from "mathjs"
import { average, linearRegression, sampleCovariance } from "simple-statistics"

describe("line regression test", () => {
  /**
   * https://whyitsso.net/math/statistics/statistics1.html
   */
  test("実験", () => {
    const data = [
      [1, 1],
      [2, 3],
      [3, 2],
      [4, 4],
      [5, 9],
    ]
    const x = data.map((d) => d[0])
    const y = data.map((d) => d[1])
    const { m, b } = linearRegression(data)
    const averageX = average(x)
    const averageY = average(y)
    const covariance = sampleCovariance(x, y)
    const varianceX = Number(variance(x))
    const varianceY = Number(variance(y))
    const slope = covariance / varianceX // slopeとinterceptはcovarianceとvarianceから求められる
    const intercept = averageY - slope * averageX // interceptはslopeとaverageから求められる
    console.log({
      m,
      b,
      covariance,
      varianceX,
      varianceY,
      slope,
      averageX,
      averageY,
    })
    expect(m).toBe(1.7)
    expect(slope).toBe(m)
    expect(b).toBe(-1.2999999999999998)
    expect(intercept).toBe(b)
  })
})