Scatter Plots, Association, and Nonlinear Patterns

Install and import#

bash

npm install fintech-algorithms

import { scatterPlotsAssociationAndNonlinearPatterns } from "fintech-algorithms/foundations/dependence-regression-and-model-foundations/scatter-plots-association-and-nonlinear-patterns";

Signature#

scatterPlotsAssociationAndNonlinearPatterns(input)

Pairs input.x and input.y into plottable points and reports the Pearson correlation over them along with its sign.

Parameters#

Name	Type	Notes
`input`	`D00Input`	One record holding the two aligned series `x` and `y`, one observation per position. x: non-empty list of finite numbers, at least two, not all identical · y: finite numbers, same length as x

Returns#

D00Output

An object with points (one { x, y } entry per observation), pearson (the correlation) and monotonicDirection, which reads positive when the correlation is above zero and negative otherwise.

Errors#

When x or y is missing, empty, or contains a non-finite number — throws RangeError
When x and y have different lengths, or fewer than two observations — the least-squares fit is computed for every topic in the family before the topic branch is taken — throws RangeError
When x is constant, which leaves the regression slope undefined — throws RangeError
When y is constant, which leaves the correlation undefined — throws RangeError

Complexity: time O(n), space O(n).

Worked example#

verified This is the worked example published in the article, replayed by the test suite on every run. The output cannot drift.

Input#

input

{
  "x": [1, 2, 3, 4, 5, 6],
  "y": [2, 3, 5, 4, 6, 7],
  "groups": ["A", "A", "A", "B", "B", "B"],
  "predictX": 7,
  "otherPredictor": [2, 4, 5, 8, 9, 13]
}

Call#

scatterPlotsAssociationAndNonlinearPatterns(input)

Returns#

object with 2 fields: points, pearson

{
  "points": [
    {
      "x": 1,
      "y": 2
    },
    {
      "x": 2,
      "y": 3
    },
    {
      "x": 3,
      "y": 5
    }
  ],
  "pearson": 0.9428571428571428
}