Correlation, Causation, Confounding, and Spurious Relationships

Install and import#

npm install fintech-algorithms

import { correlationCausationConfoundingAndSpuriousRelationships } from "fintech-algorithms/foundations/dependence-regression-and-model-foundations/correlation-causation-confounding-and-spurious-relationships";

Signature#

correlationCausationConfoundingAndSpuriousRelationships(input)

Contrasts the pooled correlation of input.x and input.y with the correlation recomputed inside each label in input.groups, which is where a confounded or reversed relationship shows itself.

Parameters#

Returns#

D00Output

An object with rawCorrelation (over all observations), withinGroupCorrelations (a map keyed by group label, whose value is null for any group with fewer than three members) and causalClaimSupported, which is always false.

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, or a group with three or more members has a constant x or y within it — throws RangeError

Complexity: time O(n*g), 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#

{
  "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#

correlationCausationConfoundingAndSpuriousRelationships(input)

Returns#

object with 2 fields: rawCorrelation, withinGroupCorrelations

{
  "rawCorrelation": 0.9428571428571428,
  "withinGroupCorrelations": {
    "A": 0.9819805060619656,
    "B": 0.9819805060619659
  }
}

Diagrams#

How it works#

This page states the contract — how to call it correctly. The article explains the concept: why it works, and where it breaks.

Read the article →

References#

• Linear Least Squares Regression — NIST/SEMATECH e-Handbook
• Correlation — NIST/SEMATECH e-Handbook
• Historical-example decision

The rest of the Dependence, Regression, and Model Foundations family#

• Scatter Plots, Association, and Nonlinear PatternsPairs input.x and input.y into plottable points and reports the Pearson correlation over them along with its sign.
• Sample Covariance Calculation and InterpretationComputes the sample covariance between input.x and input.y using the n-1 denominator, and reports which way the two series …
• Pearson Correlation Calculation and InterpretationComputes the Pearson correlation between input.x and input.y and its absolute value as a sign-free strength score.
• Spearman Rank Correlation and Kendall TauReplaces input.x and input.y with their ranks, averaging ranks across ties, then reports the Spearman correlation of those …
• Simple Ordinary Least Squares RegressionFits a single-predictor ordinary least squares line of input.y on input.x and returns the fitted coefficients with the in-s…
• Intercepts, Slopes, Coefficients, and PredictionsFits the least squares line of input.y on input.x and evaluates it at one new predictor value, input.predictX.
• Residuals, MAE, MSE, and RMSEReturns the least squares residuals of input.y on input.x together with the three usual summaries of their size.
• R-Squared and Adjusted R-SquaredReports the share of the variation in input.y that the least squares fit on input.x accounts for, and the same figure adjus…
• Regression Assumptions, Heteroskedasticity, and MulticollinearityRuns three diagnostics on the least squares fit of input.y on input.x: the mean residual, a correlation between fitted valu…