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Residuals, MAE, MSE, and RMSE

Install and import#

bash
npm install fintech-algorithms
ts
import { residualsMaeMseAndRmse } from "fintech-algorithms/foundations/dependence-regression-and-model-foundations/residuals-mae-mse-and-rmse";

Signature#

residualsMaeMseAndRmse(input)

Returns the least squares residuals of input.y on input.x together with the three usual summaries of their size.

Parameters#

NameTypeNotes
inputD00InputOne record holding the predictor series x and the outcome series y, aligned position by 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 residuals (observed minus fitted, one per observation), mae, mse and rmse.

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#

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#

residualsMaeMseAndRmse(input)

Returns#

object with 2 fields: residuals, mae

{
  "residuals": [
    -0.14285714285714324,
    -0.08571428571428585,
    0.9714285714285715,
    -0.9714285714285715,
    0.08571428571428541,
    0.14285714285714324
  ],
  "mae": 0.40000000000000013
}

Diagrams#

Residuals, MAE, MSE, and RMSE — article hero
Residuals, MAE, MSE, and RMSE — calculation ledger
Residuals, MAE, MSE, and RMSE — concept anatomy
Residuals, MAE, MSE, and RMSE — failure boundary
Residuals, MAE, MSE, and RMSE — method map
Residuals, MAE, MSE, and RMSE — scenario contrast

Calculation flow#

Reasoning flow — D00-F09-A08 
flowchart LR
    A["Synthetic input + metadata"] --> B{"Contract valid?"}
    B -->|No| C["Reject or route with reason"]
    B -->|Yes| D["Apply Residuals, MAE, MSE, and RMSE"]
    D --> E["Formula: eᵢ=yᵢ−ŷᵢ; MAE=mean|e|; MSE=mean e²; RMSE=√MSE"]
    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#

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