# Polynomial Regression Bands

> Rolling second-degree (or linear) regression of the close with bands at a multiple of the residual standard deviation, plus slope and bend values.

Updated: 2026-10-25T00:01:52.000Z · https://chartrider.com/docs/indicators/polynomial-regression-bands/

## What you see
Three lines on the price chart: the regression line (Line Color), a translucent green upper band and a translucent red lower band. Each point comes from its own fit over the candles up to that point, so later candles do not redraw earlier values. With `Show Window Curves` on, ChartRider also draws the complete fitted curve and its bands across the window of the candle under the crosshair, and puts a dot on the most recent candle in that window whose high was above, or whose low was below, the curve's band.

## How it is calculated
For every candle, with N = Regression Period and k = Band width:
1. Fit `y = a·x² + b·x + c` by least squares to the last N closes at x = 0 to N − 1; with `Linear Regression` on, fit `y = b·x + c`.
2. `regression` is the fitted curve at the newest candle (x = N − 1).
3. `σ = √(sum of (close − fit)² / N)`, the spread of the closes around the curve.
4. `upper = regression + k × σ` and `lower = regression − k × σ`.
5. `slope` is the change of the curve across the window relative to its newest value: `(newest − oldest) / newest`.
6. `bend` is the curvature from 0 to 1: `|a| × (N − 1)²` divided by the price range of the curve, compressed with `x / (x + 0.15)`. 0 is a straight line (always with linear regression), values near 1 a strongly arched curve.

With `Time Frame Multiplier` above 1, the candles are first combined into a higher timeframe (chart timeframe × multiplier, aligned to UTC).

## How to read it
- The regression line is a smoothed trend estimate that bends with price, unlike a straight regression channel.
- Closes outside the bands are stretched relative to the window's trend: candidates for mean reversion in ranges, or signs of acceleration in breakouts.
- A rising `bend` while `slope` flattens hints that the curve is turning.

## Using it in strategies
Outputs: `regression`, `upper`, `lower`, `slope` and `bend`. In the [Trade Setup](https://chartrider.com/docs/strategies/trade-setup/), "Compare" a band with the price, e.g. `lower` above the price for a close below the lower band; "Price vs line" on `regression` is a trend filter. With a multiplier, a value only counts once its higher-timeframe candle has closed. [WickScript](https://chartrider.com/docs/wickscript/) has no built-in function for it; use `use indicator "PolyReg" with period 150, periodBand 2 as pr` and read `pr.upper`, `pr.lower` and the other outputs.

## Settings

Open the settings with the slider icon next to the indicator (Indicators, `F3`). Numeric settings can be swept as Step 1 / Step 2 parameters when you run a strategy.

### Inputs

| Setting | Type | Default | Description |
|---|---|---|---|
| Regression Period | Number | `150` | Number of closes per fit (N, at least 3). (min 3) |
| Linear Regression | On/off | off | Fit a straight line instead of a parabola. |
| Show Window Curves | On/off | off | Draw the full fitted curve with its bands for the candle under the crosshair, plus dots at the latest band breaks inside that window. |
| Band width (std multiplier) | Number | `2` | Distance of the bands in standard deviations (k). 0 puts both bands on the regression line. (min 0) |
| Time Frame Multiplier) | Number | `1` | Calculate on a higher timeframe: chart timeframe × this whole number. (min 1) |

### Styles

| Setting | Type | Default | Description |
|---|---|---|---|
| Line Color | Color | `#1A4C93` |  |

## Outputs

These values can be used in Trade Setup triggers, filters and exits (see [Trade Setup](https://chartrider.com/docs/strategies/trade-setup/)) and in WickScript.

| Output | In WickScript | Description |
|---|---|---|
| regression | `regression` | End point of the fitted curve (a price). |
| upper | `upper` | Regression plus k standard deviations. |
| lower | `lower` | Regression minus k standard deviations. |
| slope | `slope` | Change of the fitted curve across the window, relative to its newest value. |
| bend | `bend` | Curvature of the fitted curve, from 0 (straight) to 1 (strongly arched). |

## Use in WickScript

`use indicator` creates this indicator inside a script, with settings by their ID. Each output is a field of the name after `as`. See [WickScript indicators](https://chartrider.com/docs/wickscript/indicators/).

```wickscript
wickscript 1
indicator "Polynomial Regression Bands from the list" on chart
use indicator "PolyReg" with period 150 as myPolyreg
show myPolyreg.regression as line "regression"
```