Regression on statili

Exponential

Mon, 01 Jan 0001 00:00:00 +0000

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# exponential function

packages/stats/src/regression/exponential.ts:49

signatures

exponential(arg1: Partial<RegressionOptions>): (args_0: DataPoint[]) => RegressionResult
exponential(suppliedOptions: Partial<RegressionOptions>, data: DataPoint[]): RegressionResult

Performs exponential regression to model the relationship y = a · e^(bx).

Captures constant proportional growth or decay — compound interest, viral spread, radioactive decay, unchecked adoption. The defining property is that Y multiplies by a fixed factor for each equal step in X, rather than adding a fixed amount as in linear regression.

Linear Regression

Mon, 01 Jan 0001 00:00:00 +0000

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# linear function

packages/stats/src/regression/linear.ts:59

signatures

linear(arg1: Partial<RegressionOptions>): (args_0: DataPoint[]) => RegressionResult
linear(suppliedOptions: Partial<RegressionOptions>, data: DataPoint[]): RegressionResult

Performs simple linear regression to model the relationship between a dependent variable (y) and an independent variable (x).

Fits a straight line (y = slope·x + intercept) through the data by minimising the sum of squared residuals between observed and predicted y values (Ordinary Least Squares).

Parameters

Name	Type	Description
suppliedOptions	Partial<RegressionOptions>	Optional overrides, e.g. `{ precision: 4 }`.
data	DataPoint[]	Array of `[x, y]` tuples. Requires at least 2 points with distinct x values.

Returns

RegressionResult

Discriminant union:

Logarithmic Regression

Mon, 01 Jan 0001 00:00:00 +0000

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# logarithmic function

packages/stats/src/regression/logarithmic.ts:48

signatures

logarithmic(arg1: Partial<RegressionOptions>): (args_0: DataPoint[]) => RegressionResult
logarithmic(suppliedOptions: Partial<RegressionOptions>, data: DataPoint[]): RegressionResult

Performs logarithmic regression to model the relationship y = a + b · ln(x).

The model captures scenarios where Y grows (or decays) rapidly at first then progressively levels off as X increases — the classic diminishing-returns pattern.

Domain constraint: x must be strictly positive (> 0). Points with x ≤ 0 are silently excluded because ln(x) is undefined for non-positive values.

Logistic Regression

Mon, 01 Jan 0001 00:00:00 +0000

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# logistic function

packages/stats/src/regression/logistic.ts:62

signatures

logistic(arg1: Partial<LogisticRegressionOptions>): (args_0: MultiDataPoint[]) => MultiRegressionResult
logistic(suppliedOptions: Partial<LogisticRegressionOptions>, data: MultiDataPoint[]): MultiRegressionResult

Performs binary logistic regression via batch gradient descent.

Models the probability that an observation belongs to class 1: P(y=1 | x) = σ(b₀ + b₁x₁ + b₂x₂ + … + bₖxₖ) where σ is the sigmoid function. Predictions at P ≥ 0.5 are classified as 1.

Multilinear Regression

Mon, 01 Jan 0001 00:00:00 +0000

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# multilinear function

packages/stats/src/regression/multilinear.ts:59

signatures

multilinear(arg1: Partial<RegressionOptions>): (args_0: MultiDataPoint[]) => MultiRegressionResult
multilinear(suppliedOptions: Partial<RegressionOptions>, data: MultiDataPoint[]): MultiRegressionResult

Performs Multiple Linear Regression (MLR) to model the relationship: y = b₀ + b₁x₁ + b₂x₂ + … + bₖxₖ

Coefficients are found by solving the normal equations: (Xᵀ X) β = Xᵀ y via Gaussian elimination with partial pivoting.

Parameters

Name	Type	Description
suppliedOptions	Partial<RegressionOptions>	Optional `{ precision }` overrides.
data	MultiDataPoint[]	Array of `{ x: number[], y: number \| null }` observations. All observations must share the same feature dimension (`x.length`). Observations with `y === null` are excluded from the fit.

Returns

MultiRegressionResult

Discriminant union:

Polynomial Regression

Mon, 01 Jan 0001 00:00:00 +0000

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# polynomial function

packages/stats/src/regression/polynomial.ts:49

signatures

polynomial(arg1: Partial<RegressionOptions>): (args_0: DataPoint[]) => RegressionResult
polynomial(suppliedOptions: Partial<RegressionOptions>, data: DataPoint[]): RegressionResult

Performs polynomial regression of configurable degree.

Fits the curve y = c₀ + c₁x + c₂x² + … + cₙxⁿ by solving the normal equations via Gaussian elimination with partial pivoting.

Parameters

Name	Type	Description
suppliedOptions	Partial<RegressionOptions>	`{ precision?, order? }` — `order` sets the polynomial degree (default 2). Increasing degree improves fit but risks overfitting when `n` is close to `order + 1`.
data	DataPoint[]	Array of `[x, y]` tuples. Requires at least `order + 1` valid points.

Returns

RegressionResult

Discriminant union:

Power Regression

Mon, 01 Jan 0001 00:00:00 +0000

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# power function

packages/stats/src/regression/power.ts:50

signatures

power(arg1: Partial<RegressionOptions>): (args_0: DataPoint[]) => RegressionResult
power(suppliedOptions: Partial<RegressionOptions>, data: DataPoint[]): RegressionResult

Performs power law regression to model the relationship y = a · xᵇ.

The model is linearised by taking logarithms of both sides: ln(y) = ln(a) + b·ln(x), which becomes a simple linear regression in log-log space. The result is then transformed back to the original scale.

Types

Mon, 01 Jan 0001 00:00:00 +0000

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# Interval interface

packages/stats/src/regression/types.ts:91

signature

interface Interval {
  /** The fitted value at x — the centre of the range. */
  fit: number;
  lower: number;
  upper: number;
}

A fitted value with an uncertainty range around it.

# LogisticRegressionOptions interface

packages/stats/src/regression/types.ts:141

signature

interface LogisticRegressionOptions {
  /** Gradient descent learning rate. @default 0.1 */
  learningRate: number;
  /** Number of gradient descent iterations. @default 1000 */
  iterations: number;
  /** Decimal places for rounding. @default 4 */
  precision: number;
}

# MultiRegressionError interface

packages/stats/src/regression/types.ts:132

signature

interface MultiRegressionError {
  ok: false;
  method?: "multilinear" | "logistic";
  errorType: RegressionErrorType;
  message: string;
}

# MultiRegressionSuccess interface

packages/stats/src/regression/types.ts:114

signature

interface MultiRegressionSuccess {
  ok: true;
  method: "multilinear" | "logistic";
  /** [intercept, b1, b2, ..., bk] */
  coefficients: number[];
  numFeatures: number;
  /** R2 for multilinear; McFadden pseudo-R2 for logistic. */
  r2: number;
  /** RMSE on training set. NaN for logistic. */
  rmse: number;
  n: number;
  points: PredictedMultiPoint[];
  predict: (x: number[]) => PredictedMultiPoint;
  equation: string;
  /** Training accuracy at 0.5 threshold (logistic only). */
  accuracy?: number;
}

# RegressionError interface

packages/stats/src/regression/types.ts:81

signature

interface RegressionError {
  ok: false;
  method?: "linear" | "logarithmic" | "exponential" | "power" | "polynomial";
  errorType: RegressionErrorType;
  message: string;
}

# RegressionOptions interface

packages/stats/src/regression/types.ts:98

signature

interface RegressionOptions {
  /** Decimal places for rounding. @default 2 */
  precision: number;
  /**
   * Confidence level for intervals, in `(0, 1)`. @default 0.95
   */
  confidenceLevel?: number;
  /** Polynomial degree (polynomial() only). @default 2 */
  order?: number;
}

# RegressionSuccess interface

packages/stats/src/regression/types.ts:11

signature

interface RegressionSuccess {
  ok: true;
  /** Primary slope / rate-of-change coefficient.
   * linear: slope m | polynomial: c1 | power: exponent b | logarithmic: ln-coeff b */
  slope: number;
  /** Y-intercept or constant term.
   * linear: y-int | polynomial: c0 | power: scale a | logarithmic: constant a */
  intercept: number;
  /** Coefficient of determination R2 in [0,1]. */
  r2: number;
  /** Root Mean Squared Error in the same units as Y. */
  rmse: number;
  /** Number of valid data points used. */
  n: number;
  method: "linear" | "logarithmic" | "exponential" | "power" | "polynomial";
  points: PredictedPoint[];
  predict: (x: number) => PredictedPoint;
  /** Full coefficient vector [c0,c1,...,cn] for polynomial. */
  coefficients?: number[];
  /** Polynomial degree. */
  degree?: number;
  /** Human-readable equation string. */
  equation?: string;
  // ── Inference on the slope ──────────────────────────────────────────────
  // Populated by `linear()` only. Left `undefined` by every other method —
  // polynomial needs the full coefficient covariance matrix, and the
  // log-linearised fits (power, logarithmic) would report significance in
  // transformed space, which is not what a caller would expect.
  //
  // All four are `null` when there are too few points to estimate them
  // (`n < 3`, i.e. `df < 1`), and `tM`/`pValueM` are additionally `null` for a
  /
// …truncated

Type shortened for readability — see the source for the full definition.