Linear Regression Channel

1. Summary (Introduction)

The Linear Regression Channel is a technical analysis tool that consists of three parallel lines plotted on a price chart. It is a statistically-based indicator that uses the linear regression (or "least squares fit") method to determine the primary trend direction.

The Middle Line is the actual linear regression trendline.
The Upper and Lower Channel Lines are plotted a specified number of standard deviations above and below the middle line.

The indicator provides an objective, mathematical measure of a trend and its trading channel, helping traders to identify trend direction, dynamic support and resistance levels, and potential overbought/oversold conditions relative to the trend.

2. Mathematical Foundations and Calculation Logic

The indicator's core is the linear regression trendline, which is the straight line that best fits a series of data points (in this case, prices) over a specified period.

Required Components

Period (N): The lookback period for the regression calculation (e.g., 100).
Price Data (P): The price series used for the calculation. The standard implementation uses the Close price.
Deviations (M): The number of standard deviations to shift the channel lines away from the middle line.

Calculation Steps (Algorithm)

For the last N bars at any given point in time:

Calculate the Linear Regression Line: Using the method of least squares, find the straight line that minimizes the distance to each of the N price points. This line is defined by its slope (b) and y-intercept (a). \text{Regression Line}_t = a + b \times t (where t is the time index from 0 to N-1)
Calculate the Standard Deviation: Compute the standard deviation of the N price points from the calculated regression line. This measures the average dispersion or volatility around the trendline. \sigma = \sqrt{\frac{\sum_{k=1}^{N} (P_k - \text{Regression Line}_k)^2}{N}}
Calculate the Upper and Lower Channel Lines: Add and subtract a multiple of the standard deviation from the regression line. \text{Upper Channel}_t = \text{Regression Line}_t + (M \times \sigma) \text{Lower Channel}_t = \text{Regression Line}_t - (M \times \sigma)

Important Note on "Repainting": The Linear Regression Channel is a "repainting" indicator by nature. Because the entire line is recalculated for the most recent N bars every time a new bar forms, its position in the recent past can change. This is not a bug but a fundamental characteristic of the statistical method.

3. MQL5 Implementation Details

Our MQL5 implementation is designed to be highly efficient and visually clean by leveraging MetaTrader 5's built-in graphical objects.

Object-Based Plotting: Instead of using indicator buffers, our indicator uses a single, built-in OBJ_REGRESSION graphical object. This object is managed by the MetaTrader terminal, which handles the complex regression and standard deviation calculations internally using highly optimized code.
Clean, Non-Continuous Display: By default, the indicator only displays the single, most current regression channel calculated on the last N bars. This provides a clean, uncluttered view of the present market structure.
Efficient "On New Bar" Updates: The indicator is designed to be extremely light on terminal resources. It uses a simple time-check within OnCalculate. The channel object is only updated once per bar, when a new candle forms, preventing unnecessary recalculations on every tick.
Automatic Cleanup (RAII): The graphical object is given a unique name upon creation. The OnDeinit function ensures that this object is always deleted from the chart when the indicator is removed, leaving no visual artifacts behind.
Heikin Ashi Variant: A "pure" Heikin Ashi version can be created by calculating the Heikin Ashi prices into an array and then manually performing the regression calculation on that array (as the built-in OBJ_REGRESSION object cannot be pointed to a custom data source).

4. Parameters

Regression Period (InpRegressionPeriod): The number of bars to include in the regression calculation. A longer period creates a more stable, long-term trendline, while a shorter period is more responsive to recent price action. Default is 100.
Deviations (InpDeviations): The multiplier for the standard deviation, which determines the width of the channel. Default is 2.0.
Channel Extensions:
- InpRayRight: If true, the calculated channel will be extended indefinitely into the future, which can be used to project potential future support and resistance levels. Default is false.
- InpRayLeft: If true, the channel will be extended indefinitely into the past. Default is false.

5. Usage and Interpretation

Trend Identification: The slope of the middle line indicates the direction of the trend. An upward slope is bullish; a downward slope is bearish.
Dynamic Support and Resistance: The channel lines act as dynamic support and resistance levels. In an uptrend, the lower line can be seen as a buy zone. In a downtrend, the upper line can be seen as a sell zone.
Overbought/Oversold: A move to the upper channel line can be considered overbought relative to the current trend, while a move to the lower line can be considered oversold.
Breakouts: A strong close outside the channel can signal that the current trend is accelerating or that a reversal is imminent.
Caution: Due to its repainting nature, signals should be interpreted with care. A historical price touch of a channel line may not have appeared the same way in real-time. The indicator is best used for confirming the current market structure rather than for generating precise entry signals from past data.

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