LinRegIntercept

Linear Regression Intercept (LINEARREG_INTERCEPT) — the intercept a of the rolling least-squares fit y = a + b·x over the last period inputs.

Quick reference

Field	Value
Family	Price Statistics
Input type	f64 (single close)
Output type	f64
Output range	unbounded (price scale)
Default parameters	period is required
Warmup period	period
Interpretation	The fitted trend line's value at the start of the window — where the regression says the series began.

Formula

Over the last period inputs, indexed x = 0, 1, …, period − 1, fit y = a + b·x by ordinary least squares:

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

LinRegIntercept reports a — the fitted line at x = 0, the oldest point in the window. Where LinearRegression evaluates the fit at the most recent bar (a + b·(period − 1)), this reports its value at the window's start. Because the x values are fixed, Σx and Σxx are constants and each update is O(1) over a sliding window. See crates/wickra-core/src/indicators/linreg_intercept.rs.

Parameters

Name	Type	Default	Valid range	Description	Source
period	usize	none	>= 2	Regression window length. period < 2 errors with Error::InvalidPeriod (a line needs at least two points).	linreg_intercept.rs:51

Inputs / Outputs

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

use wickra::{Indicator, LinRegIntercept};
// LinRegIntercept: Input = f64, Output = f64
const _: fn(&mut LinRegIntercept, f64) -> Option<f64> = <LinRegIntercept as Indicator>::update;

Python streams as float | None, batches as an array.array('d') (NaN for warmup). Node streams as number | null, batches as Array<number> with NaN placeholders.

Warmup

LinRegIntercept::new(period).warmup_period() == period. The first value is emitted once period points fill the window. The unit tests accessors_report_config and reference_value (which asserts out[0] and out[1] are None for period = 3) pin this.

Edge cases

• Exact fit on a straight line. For collinear inputs the regression is exact and the intercept is the line's y at x = 0. The unit test slides_and_tracks_a_shifted_line pins this (window [10, 12, 14] → y = 10 + 2x, intercept 10).
• Short period. LinRegIntercept::new(1) returns Err(Error::InvalidPeriod). The unit test rejects_short_period pins this.
• Reset. lr.reset() clears the window and the running sums. The unit test reset_clears_state pins this.

Examples

Rust

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

fn main() -> Result<(), Box<dyn std::error::Error>> {
    let mut lr = LinRegIntercept::new(3)?;
    let out: Vec<Option<f64>> = lr.batch(&[1.0, 2.0, 9.0]);
    println!("{:?}", out);
    Ok(())
}

Output:

[None, None, Some(0.0)]

Period 3 over [1, 2, 9]: the least-squares fit is y = 0 + 4x, so the intercept at x = 0 is 0.0. This matches the reference_value unit test in crates/wickra-core/src/indicators/linreg_intercept.rs.

Python

import numpy as np
import wickra as ta

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

Output:

[nan nan  0.]

Node

const ta = require('wickra');
const lr = new ta.LINEARREG_INTERCEPT(3);
for (const x of [1, 2, 9]) console.log(x, '->', lr.update(x));

Output:

1 -> null
2 -> null
9 -> 0

Interpretation

LinRegIntercept answers "given the recent trend, where did the window start?" Together with LinRegSlope it fully describes the fitted line: intercept is the anchor at x = 0, slope is the per-bar drift. Comparing the intercept to the current price shows how far price has travelled from the regression's starting point over the window. It is most useful as a component of regression channels and as a feature, rather than a standalone signal.

Prefer LinearRegression when you want the fitted value at the current bar, and Tsf when you want it projected one bar ahead.

Common pitfalls

• Reading it as a current level. The intercept is anchored at the oldest bar of the window (x = 0), not the latest; on a trending series it can sit far from the current price by design.
• Period < 2. A regression line is undefined for a single point — the constructor rejects it rather than returning a degenerate value.

References

The Linear Regression Intercept is TA-Lib's LINEARREG_INTERCEPT function; the closed-form OLS coefficients are standard least-squares results.

See also

• Indicator-LinearRegression — the fit at the current bar.
• Indicator-LinRegSlope — the slope b.
• Indicator-Tsf — the fit projected one bar ahead.
• Indicators-Overview — the full taxonomy.