wickra/docs/wiki/indicators/price-statistics/Indicator-LinearRegression.md

LinearRegression

Linear Regression — the endpoint of a rolling ordinary-least-squares fit over the last period prices.

Quick reference

Field	Value
Family	Price Statistics
Input type	f64 (price)
Output type	f64
Output range	unbounded (price scale)
Default parameters	period = 14 (Python)
Warmup period	period
Interpretation	A low-lag smoothed price — the trend line extrapolated to now.

Formula

Over the last period inputs, indexed x = 0, 1, …, period − 1:

b (slope)     = (n·Σxy − Σx·Σy) / (n·Σxx − (Σx)²)
a (intercept) = (Σy − b·Σx) / n
LinearReg     = a + b·(period − 1)

The indicator fits a straight line to the window by ordinary least squares, then reports that line's value at the most recent bar. Because it extrapolates the local trend forward rather than averaging it away, it lags a same-period Sma noticeably less. This is TA-Lib's LINEARREG.

Parameters

period — the regression window. Must be at least 2 (a line needs two points). The Python binding defaults it to 14; the Rust and Node constructors require it explicitly.

Inputs / Outputs

From crates/wickra-core/src/indicators/linreg.rs:

impl Indicator for LinearRegression {
    type Input = f64;
    type Output = f64;
    // update(&mut self, input: f64) -> Option<f64>
}

LinearRegression is a scalar indicator: it consumes one f64 price per step. Because Input = f64 it can sit inside a Chain.

Warmup

LinearRegression::new(14).warmup_period() == 14. The first value lands once the window holds a full period prices — on input index period − 1.

Complexity

Each update is O(1): the Σx and Σxx terms depend only on period and are precomputed once at construction, and Σy / Σxy are maintained incrementally as the window slides via the closed-form identity new_Σxy = old_Σxy − old_Σy + popped_y₀ (then Σxy += (n − 1) · new_value and Σy += new_value). The same applies to LinRegSlope and LinRegAngle.

Edge cases

• period < 2. Rejected at construction — a regression line is undefined for fewer than two points.
• Perfect line. Fed a perfectly linear series, the fit is that line, so the endpoint equals the current value (perfect_line_returns_current_value pins this).
• Constant series. A flat input returns that constant.
• Reset. lr.reset() clears the rolling window and the running Σy / Σxy accumulators.

Examples

Rust

use wickra::{BatchExt, Indicator, LinearRegression};

fn main() -> Result<(), Box<dyn std::error::Error>> {
    let mut lr = LinearRegression::new(3)?;
    // Fit over [1, 2, 9]: the least-squares line is y = 4x, endpoint 4·2 = 8.
    let out = lr.batch(&[1.0, 2.0, 9.0]);
    println!("{:?}", out);
    Ok(())
}

Output:

[None, None, Some(8.0)]

This matches the reference_values test in crates/wickra-core/src/indicators/linreg.rs.

Python

import numpy as np
import wickra as ta

lr = ta.LinearRegression(3)
print(lr.batch(np.array([1.0, 2.0, 9.0])))

Output:

[nan nan  8.]

Node

const ta = require('wickra');
const lr = new ta.LinearRegression(3);
console.log(lr.batch([1, 2, 9]));

Output:

[ NaN, NaN, 8 ]

Interpretation

Read LinearRegression as a low-lag moving average: it tracks price more closely than an SMA of the same period because it projects the window's trend to the current bar instead of centring on the window. A shorter period hugs price; a longer one is a smoother trend line. Pair it with LinRegSlope to read the same fit's steepness.

Common pitfalls

• Confusing it with an SMA. It is a projected fit, not a centred average, so it leads an SMA of the same period.
• Tiny periods. period = 2 is allowed but the "fit" just passes through the last two points; use a meaningful window.

References

Ordinary least-squares linear regression applied to a rolling price window; the endpoint formulation matches TA-Lib's LINEARREG.

See also

• Indicator-LinRegSlope.md — the slope of the same rolling fit.
• Indicator-Sma.md — the centred average it is often compared against.
• Indicators-Overview.md — the full taxonomy.