Python's statistics.linear_regression in TypeScript

How to use

Install via yarn add locutus and import: import { linear_regression } from 'locutus/python/statistics/linear_regression'.

Or with CommonJS: const { linear_regression } = require('locutus/python/statistics/linear_regression')

Use a bundler that supports tree-shaking so you only ship the functions you actually use. Vite, webpack, Rollup, and Parcel all handle this. For server-side use this is less of a concern.

Examples

These examples are extracted from test cases that automatically verify our functions against their native counterparts.

#	code	expected result
1	linear_regression([1, 2, 3], [2, 4, 6])	{slope: 2, intercept: 0}
2	linear_regression([1, 2, 3], [1, 2, 2])	{slope: 0.5, intercept: 0.6666666666666667}
3	linear_regression([1, 2, 3], [2, 4, 6], true)	{slope: 2, intercept: 0}

Notes

• Returns ordinary least-squares slope and intercept, mirroring Python’s named tuple as a plain object.

Dependencies

This function uses the following Locutus functions:

• _statistics (python/_helpers)

Here's what our current TypeScript equivalent to Python's statistics.linear_regression looks like.

TSTypeScript JSJavaScript TSStandalone TS JSStandalone JS

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import {
  assertStatisticsArray,
  statisticsMeanFromSequence,
  sumProducts,
  toStatisticNumber,
} from '../_helpers/_statistics.ts'

export function linear_regression(x: unknown, y: unknown, proportional = false): { slope: number; intercept: number } {
  //      discuss at: https://locutus.io/python/statistics/linear_regression/
  // parity verified: Python 3.12
  //     original by: Kevin van Zonneveld (https://kvz.io)
  //          note 1: Returns ordinary least-squares slope and intercept, mirroring Python's named tuple as a plain object.
  //       example 1: linear_regression([1, 2, 3], [2, 4, 6])
  //       returns 1: {slope: 2, intercept: 0}
  //       example 2: linear_regression([1, 2, 3], [1, 2, 2])
  //       returns 2: {slope: 0.5, intercept: 0.6666666666666667}
  //       example 3: linear_regression([1, 2, 3], [2, 4, 6], true)
  //       returns 3: {slope: 2, intercept: 0}

  const xValues = assertStatisticsArray(x, 'linear_regression').map((value) =>
    toStatisticNumber(value, 'linear_regression'),
  )
  const yValues = assertStatisticsArray(y, 'linear_regression').map((value) =>
    toStatisticNumber(value, 'linear_regression'),
  )

  const n = xValues.length
  if (yValues.length !== n) {
    throw new Error('linear regression requires that both inputs have same number of data points')
  }
  if (n < 2) {
    throw new Error('linear regression requires at least two data points')
  }

  if (proportional) {
    const sxy = sumProducts(xValues, yValues) + 0
    const sxx = sumProducts(xValues, xValues)
    if (sxx === 0) {
      throw new Error('x is constant')
    }
    return { slope: sxy / sxx, intercept: 0 }
  }

  const xbar = statisticsMeanFromSequence({
    values: xValues,
    integral: xValues.every(Number.isInteger),
  })
  const ybar = statisticsMeanFromSequence({
    values: yValues,
    integral: yValues.every(Number.isInteger),
  })

  const centeredX = xValues.map((value) => value - xbar)
  const centeredY = yValues.map((value) => value - ybar)
  const sxy = sumProducts(centeredX, centeredY) + 0
  const sxx = sumProducts(centeredX, centeredX)
  if (sxx === 0) {
    throw new Error('x is constant')
  }

  const slope = sxy / sxx
  return {
    slope,
    intercept: ybar - slope * xbar,
  }
}

import {
  assertStatisticsArray,
  statisticsMeanFromSequence,
  sumProducts,
  toStatisticNumber,
} from '../_helpers/_statistics.ts'

export function linear_regression(x, y, proportional = false) {
  //      discuss at: https://locutus.io/python/statistics/linear_regression/
  // parity verified: Python 3.12
  //     original by: Kevin van Zonneveld (https://kvz.io)
  //          note 1: Returns ordinary least-squares slope and intercept, mirroring Python's named tuple as a plain object.
  //       example 1: linear_regression([1, 2, 3], [2, 4, 6])
  //       returns 1: {slope: 2, intercept: 0}
  //       example 2: linear_regression([1, 2, 3], [1, 2, 2])
  //       returns 2: {slope: 0.5, intercept: 0.6666666666666667}
  //       example 3: linear_regression([1, 2, 3], [2, 4, 6], true)
  //       returns 3: {slope: 2, intercept: 0}

  const xValues = assertStatisticsArray(x, 'linear_regression').map((value) =>
    toStatisticNumber(value, 'linear_regression'),
  )
  const yValues = assertStatisticsArray(y, 'linear_regression').map((value) =>
    toStatisticNumber(value, 'linear_regression'),
  )

  const n = xValues.length
  if (yValues.length !== n) {
    throw new Error('linear regression requires that both inputs have same number of data points')
  }
  if (n < 2) {
    throw new Error('linear regression requires at least two data points')
  }

  if (proportional) {
    const sxy = sumProducts(xValues, yValues) + 0
    const sxx = sumProducts(xValues, xValues)
    if (sxx === 0) {
      throw new Error('x is constant')
    }
    return { slope: sxy / sxx, intercept: 0 }
  }

  const xbar = statisticsMeanFromSequence({
    values: xValues,
    integral: xValues.every(Number.isInteger),
  })
  const ybar = statisticsMeanFromSequence({
    values: yValues,
    integral: yValues.every(Number.isInteger),
  })

  const centeredX = xValues.map((value) => value - xbar)
  const centeredY = yValues.map((value) => value - ybar)
  const sxy = sumProducts(centeredX, centeredY) + 0
  const sxx = sumProducts(centeredX, centeredX)
  if (sxx === 0) {
    throw new Error('x is constant')
  }

  const slope = sxy / sxx
  return {
    slope,
    intercept: ybar - slope * xbar,
  }
}

// python/_helpers/_statistics (Locutus helper dependency)
type NumericSequence = {
  values: number[]
  integral: boolean
}

function assertStatisticsArray(data: unknown, functionName: string): unknown[] {
  if (!Array.isArray(data)) {
    throw new TypeError(`${functionName}() data must be an array`)
  }

  return data
}

function toStatisticNumber(value: unknown, functionName: string): number {
  if (typeof value === 'number') {
    return value
  }

  if (typeof value === 'boolean') {
    return value ? 1 : 0
  }

  if (typeof value === 'bigint') {
    const numericValue = Number(value)
    if (!Number.isSafeInteger(numericValue)) {
      throw new RangeError(`${functionName}() bigint values must fit within JS safe integers`)
    }

    return numericValue
  }

  throw new TypeError(`${functionName}() data must contain only real numbers`)
}

function statisticsMeanFromSequence(sequence: NumericSequence, preferFloat = false): number {
  return divideStatisticsValue(sumNumbers(sequence.values), sequence.values.length, sequence.integral, preferFloat)
}

function sumNumbers(values: number[]): number {
  return values.reduce((sum, value) => sum + value, 0)
}

function sumProducts(left: number[], right: number[]): number {
  let total = 0
  for (let index = 0; index < left.length; index += 1) {
    total += (left[index] ?? 0) * (right[index] ?? 0)
  }
  return total
}

function divideStatisticsValue(total: number, divisor: number, integral: boolean, preferFloat = false): number {
  if (!preferFloat && integral && Number.isSafeInteger(total) && total % divisor === 0) {
    return total / divisor
  }

  return total / divisor
}

// python/statistics/linear_regression (target function module)
function linear_regression(x: unknown, y: unknown, proportional = false): { slope: number; intercept: number } {
  //      discuss at: https://locutus.io/python/statistics/linear_regression/
  // parity verified: Python 3.12
  //     original by: Kevin van Zonneveld (https://kvz.io)
  //          note 1: Returns ordinary least-squares slope and intercept, mirroring Python's named tuple as a plain object.
  //       example 1: linear_regression([1, 2, 3], [2, 4, 6])
  //       returns 1: {slope: 2, intercept: 0}
  //       example 2: linear_regression([1, 2, 3], [1, 2, 2])
  //       returns 2: {slope: 0.5, intercept: 0.6666666666666667}
  //       example 3: linear_regression([1, 2, 3], [2, 4, 6], true)
  //       returns 3: {slope: 2, intercept: 0}

  const xValues = assertStatisticsArray(x, 'linear_regression').map((value) =>
    toStatisticNumber(value, 'linear_regression'),
  )
  const yValues = assertStatisticsArray(y, 'linear_regression').map((value) =>
    toStatisticNumber(value, 'linear_regression'),
  )

  const n = xValues.length
  if (yValues.length !== n) {
    throw new Error('linear regression requires that both inputs have same number of data points')
  }
  if (n < 2) {
    throw new Error('linear regression requires at least two data points')
  }

  if (proportional) {
    const sxy = sumProducts(xValues, yValues) + 0
    const sxx = sumProducts(xValues, xValues)
    if (sxx === 0) {
      throw new Error('x is constant')
    }
    return { slope: sxy / sxx, intercept: 0 }
  }

  const xbar = statisticsMeanFromSequence({
    values: xValues,
    integral: xValues.every(Number.isInteger),
  })
  const ybar = statisticsMeanFromSequence({
    values: yValues,
    integral: yValues.every(Number.isInteger),
  })

  const centeredX = xValues.map((value) => value - xbar)
  const centeredY = yValues.map((value) => value - ybar)
  const sxy = sumProducts(centeredX, centeredY) + 0
  const sxx = sumProducts(centeredX, centeredX)
  if (sxx === 0) {
    throw new Error('x is constant')
  }

  const slope = sxy / sxx
  return {
    slope,
    intercept: ybar - slope * xbar,
  }
}

// python/_helpers/_statistics (Locutus helper dependency)
function assertStatisticsArray(data, functionName) {
  if (!Array.isArray(data)) {
    throw new TypeError(`${functionName}() data must be an array`)
  }

  return data
}

function toStatisticNumber(value, functionName) {
  if (typeof value === 'number') {
    return value
  }

  if (typeof value === 'boolean') {
    return value ? 1 : 0
  }

  if (typeof value === 'bigint') {
    const numericValue = Number(value)
    if (!Number.isSafeInteger(numericValue)) {
      throw new RangeError(`${functionName}() bigint values must fit within JS safe integers`)
    }

    return numericValue
  }

  throw new TypeError(`${functionName}() data must contain only real numbers`)
}

function statisticsMeanFromSequence(sequence, preferFloat = false) {
  return divideStatisticsValue(sumNumbers(sequence.values), sequence.values.length, sequence.integral, preferFloat)
}

function sumNumbers(values) {
  return values.reduce((sum, value) => sum + value, 0)
}

function sumProducts(left, right) {
  let total = 0
  for (let index = 0; index < left.length; index += 1) {
    total += (left[index] ?? 0) * (right[index] ?? 0)
  }
  return total
}

function divideStatisticsValue(total, divisor, integral, preferFloat = false) {
  if (!preferFloat && integral && Number.isSafeInteger(total) && total % divisor === 0) {
    return total / divisor
  }

  return total / divisor
}

// python/statistics/linear_regression (target function module)
function linear_regression(x, y, proportional = false) {
  //      discuss at: https://locutus.io/python/statistics/linear_regression/
  // parity verified: Python 3.12
  //     original by: Kevin van Zonneveld (https://kvz.io)
  //          note 1: Returns ordinary least-squares slope and intercept, mirroring Python's named tuple as a plain object.
  //       example 1: linear_regression([1, 2, 3], [2, 4, 6])
  //       returns 1: {slope: 2, intercept: 0}
  //       example 2: linear_regression([1, 2, 3], [1, 2, 2])
  //       returns 2: {slope: 0.5, intercept: 0.6666666666666667}
  //       example 3: linear_regression([1, 2, 3], [2, 4, 6], true)
  //       returns 3: {slope: 2, intercept: 0}

  const xValues = assertStatisticsArray(x, 'linear_regression').map((value) =>
    toStatisticNumber(value, 'linear_regression'),
  )
  const yValues = assertStatisticsArray(y, 'linear_regression').map((value) =>
    toStatisticNumber(value, 'linear_regression'),
  )

  const n = xValues.length
  if (yValues.length !== n) {
    throw new Error('linear regression requires that both inputs have same number of data points')
  }
  if (n < 2) {
    throw new Error('linear regression requires at least two data points')
  }

  if (proportional) {
    const sxy = sumProducts(xValues, yValues) + 0
    const sxx = sumProducts(xValues, xValues)
    if (sxx === 0) {
      throw new Error('x is constant')
    }
    return { slope: sxy / sxx, intercept: 0 }
  }

  const xbar = statisticsMeanFromSequence({
    values: xValues,
    integral: xValues.every(Number.isInteger),
  })
  const ybar = statisticsMeanFromSequence({
    values: yValues,
    integral: yValues.every(Number.isInteger),
  })

  const centeredX = xValues.map((value) => value - xbar)
  const centeredY = yValues.map((value) => value - ybar)
  const sxy = sumProducts(centeredX, centeredY) + 0
  const sxx = sumProducts(centeredX, centeredX)
  if (sxx === 0) {
    throw new Error('x is constant')
  }

  const slope = sxy / sxx
  return {
    slope,
    intercept: ybar - slope * xbar,
  }
}

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