151 lines
4.0 KiB
Markdown
151 lines
4.0 KiB
Markdown
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# LinRegSlope
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> Linear Regression Slope — the slope of a rolling ordinary-least-squares
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> fit over the last `period` prices.
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## Quick reference
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| Field | Value |
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|-------|-------|
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| Family | Statistics |
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| Sub-category | Regression |
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| Input type | `f64` (price) |
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| Output type | `f64` |
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| Output range | unbounded around zero (price units per bar) |
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| Default parameters | `period = 14` (Python) |
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| Warmup period | `period` |
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| Interpretation | How steeply price trends; positive up, negative down, zero flat. |
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## Formula
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Over the last `period` inputs, indexed `x = 0, 1, …, period − 1`:
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```
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b = (n·Σxy − Σx·Σy) / (n·Σxx − (Σx)²)
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```
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`LinRegSlope` fits a straight line to the window by ordinary least squares —
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the same fit as [`LinearRegression`](Indicator-LinearRegression.md) — but
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reports the *slope* `b` instead of the endpoint. The slope is in price units
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per bar: positive while price trends up, negative while it trends down, near
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zero when it is ranging. This is TA-Lib's `LINEARREG_SLOPE`.
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## Parameters
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`period` — the regression window. Must be at least `2` (a line needs two
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points). The Python binding defaults it to `14`; the Rust and Node
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constructors require it explicitly.
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## Inputs / Outputs
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From `crates/wickra-core/src/indicators/linreg_slope.rs`:
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```rust
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impl Indicator for LinRegSlope {
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type Input = f64;
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type Output = f64;
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// update(&mut self, input: f64) -> Option<f64>
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}
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```
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`LinRegSlope` is a **scalar** indicator: it consumes one `f64` price per step.
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Because `Input = f64` it can sit inside a [`Chain`](../../Indicator-Chaining.md).
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## Warmup
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`LinRegSlope::new(14).warmup_period() == 14`. The first value lands once the
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window holds a full `period` prices — on input index `period − 1`.
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## Edge cases
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- **`period < 2`.** Rejected at construction — a regression line is undefined
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for fewer than two points.
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- **Perfect line.** Fed a series rising by a fixed step, the slope is exactly
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that step (`perfect_line_returns_its_step` pins this).
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- **Constant series.** A flat input returns a slope of `0`.
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- **Falling series.** A descending input returns a negative slope.
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- **Reset.** `ls.reset()` clears the rolling window.
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## Examples
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### Rust
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```rust
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use wickra::{BatchExt, Indicator, LinRegSlope};
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fn main() -> Result<(), Box<dyn std::error::Error>> {
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let mut ls = LinRegSlope::new(3)?;
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// Fit over [1, 2, 9]: the least-squares line is y = 4x, slope 4.
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let out = ls.batch(&[1.0, 2.0, 9.0]);
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println!("{:?}", out);
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Ok(())
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}
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```
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Output:
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```
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[None, None, Some(4.0)]
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```
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This matches the `reference_values` test in
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`crates/wickra-core/src/indicators/linreg_slope.rs`.
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### Python
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```python
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import numpy as np
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import wickra as ta
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ls = ta.LinRegSlope(3)
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print(ls.batch(np.array([1.0, 2.0, 9.0])))
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```
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Output:
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```
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[nan nan 4.]
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```
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### Node
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```javascript
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const ta = require('wickra');
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const ls = new ta.LinRegSlope(3);
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console.log(ls.batch([1, 2, 9]));
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```
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Output:
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```
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[ NaN, NaN, 4 ]
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```
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## Interpretation
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`LinRegSlope` is a momentum gauge: its sign is the trend direction and its
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magnitude is the trend's steepness in price-per-bar. A slope crossing zero
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marks a trend change; a slope that flattens while price still rises warns the
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trend is losing pace. Unlike a difference-based oscillator it uses every bar
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in the window, so it is less jumpy.
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## Common pitfalls
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- **Comparing slopes across instruments.** The slope is in the instrument's
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own price units per bar — normalise (e.g. divide by price) to compare.
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- **Tiny periods.** `period = 2` reduces the slope to the last simple
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difference; use a meaningful window.
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## References
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The slope of an ordinary least-squares fit to a rolling price window; matches
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TA-Lib's `LINEARREG_SLOPE`.
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## See also
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- [Indicator-LinearRegression.md](Indicator-LinearRegression.md) — the
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endpoint of the same rolling fit.
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- [Indicator-Mom.md](../momentum/Indicator-Mom.md) — raw price-difference
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momentum, the unsmoothed cousin.
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- [Indicators-Overview.md](../../Indicators-Overview.md) — the full taxonomy.
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