Sample Covariance Calculation and Interpretation

Install and import#

npm install fintech-algorithms

import { sampleCovarianceCalculationAndInterpretation } from "fintech-algorithms/foundations/dependence-regression-and-model-foundations/sample-covariance-calculation-and-interpretation";

Signature#

sampleCovarianceCalculationAndInterpretation(input)

Computes the sample covariance between input.x and input.y using the n-1 denominator, and reports which way the two series move together.

Parameters#

Returns#

D00Output

An object with sampleCovariance and direction, which reads positive when the covariance is above zero and negative otherwise, exactly zero included.

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

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#

{
  "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#

sampleCovarianceCalculationAndInterpretation(input)

Returns#

object with 2 fields: sampleCovariance, direction

{
  "sampleCovariance": 3.3,
  "direction": "positive"
}

Diagrams#

Calculation flow#

flowchart LR
    A["Synthetic input + metadata"] --> B{"Contract valid?"}
    B -->|No| C["Reject or route with reason"]
    B -->|Yes| D["Apply Sample Covariance Calculation and Interpretation"]
    D --> E["Formula: sxy=Σ(xᵢ−x̄)(yᵢ−ȳ)/(n−1)"]
    E --> F["Verified fixture output"]
    F --> G{"Interpretation within boundary?"}
    G -->|Yes| H["Report value + convention + audit"]
    G -->|No| I["Add companion view or narrower claim"]

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.
• 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 …
• Correlation, Causation, Confounding, and Spurious RelationshipsContrasts the pooled correlation of input.x and input.y with the correlation recomputed inside each label in input.groups…
• 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…