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+# Linear Regression Pro
+
+## 1. Summary (Introduction)
+
+The Linear Regression Pro is a highly flexible, manually calculated version of the classic Linear Regression Channel. It is a statistically-based indicator that uses the **linear regression** (or "least squares fit") method to determine the primary trend direction.
+
+Unlike the built-in MetaTrader 5 graphical objects, this "Pro" version offers full customization over its calculation, including the **source price** and the **channel width calculation method**. It is designed to be a robust, efficient, and precise tool for advanced technical analysis.
+
+- The **Middle Line** is the linear regression trendline.
+- The **Upper and Lower Channel Lines** are plotted based on a selected deviation method.
+
+## 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 over a specified period.
+
+### Required Components
+
+- **Period (N):** The lookback period for the regression calculation.
+- **Source Price (P):** The price series used for the calculation (e.g., Close, Typical, etc.).
+- **Channel Mode:** The method for calculating the channel width.
+- **Deviations (M):** The multiplier for the standard deviation (used in Standard Deviation mode).
+
+### Calculation Steps (Algorithm)
+
+For the last `N` bars at any given point in time:
+
+1. **Calculate the Linear Regression Line:** Using the method of least squares, find the straight line that best fits the `N` source price points.
+   $\text{Regression Line}_t = a + b \times t$
+
+2. **Calculate the Channel Width (Deviation Offset):** Based on the selected `Channel Mode`:
+
+   - **Standard Deviation Mode:** Compute the standard deviation of the `N` price points from the calculated regression line.
+     $\sigma = \sqrt{\frac{\sum_{k=1}^{N} (P_k - \text{Regression Line}_k)^2}{N}}$
+     $\text{Offset} = M \times \sigma$
+   - **Maximum Deviation Mode:** Find the largest absolute distance between any of the `N` price points and the regression line.
+     $\text{Offset} = \text{Max}(\text{Abs}(P_k - \text{Regression Line}_k))$
+
+3. **Calculate the Upper and Lower Channel Lines:** Add and subtract the calculated `Offset` from the regression line.
+   $\text{Upper Channel}_t = \text{Regression Line}_t + \text{Offset}$
+   $\text{Lower Channel}_t = \text{Regression Line}_t - \text{Offset}$
+
+## 3. MQL5 Implementation Details
+
+Our MQL5 implementation is a completely self-contained, robust, and accurate indicator.
+
+- **Stability via Full Recalculation:** We employ a "brute-force" full recalculation model.
+- **Fully Manual Calculations:** All calculations, including the regression line and both deviation methods, are performed **manually**. This provides maximum flexibility and ensures the indicator is independent of the limitations and potential inconsistencies of built-in graphical objects.
+- **Efficient "On New Bar" Updates:** The indicator is designed to be extremely light on terminal resources. The entire complex calculation is only performed **once per bar** when a new candle forms, preventing unnecessary CPU load on every tick.
+- **Clean, Non-Continuous Display:** The indicator only displays the **single, most current** regression channel calculated on the last `N` bars. This is achieved by dynamically setting the `PLOT_DRAW_BEGIN` property on each update, providing a clean, uncluttered view of the present market structure.
+
+### Indicator Family
+
+- **`LinearRegression_Pro.mq5`:** The standard version, which can be configured to use any `ENUM_APPLIED_PRICE`.
+- **`LinearRegression_Pro_Sample.mq5`:** An educational variant that uses the **Sample Standard Deviation** (`n-1` in the denominator) instead of the Population Standard Deviation (`n`). This version produces slightly wider channels, similar to the built-in `OBJ_STDDEVCHANNEL` object in MetaTrader.
+- **`LinearRegression_Pro_HeikinAshi.mq5`:** The "pure" Heikin Ashi version, where the regression is calculated on the smoothed Heikin Ashi price data.
+
+## 4. Parameters
+
+- **Regression Period (`InpRegressionPeriod`):** The number of bars to include in the calculation.
+- **Applied Price (`InpAppliedPrice`):** The source price for the calculation (e.g., `PRICE_CLOSE`, `PRICE_TYPICAL`).
+- **Channel Mode (`InpChannelMode`):** Allows the user to select the method for calculating the channel width:
+  - `DEVIATION_STANDARD`: Based on the standard deviation (most common).
+  - `DEVIATION_MAXIMUM`: Based on the maximum price deviation.
+- **Deviations (`InpDeviations`):** The multiplier for the standard deviation, used only when `DEVIATION_STANDARD` mode is selected.
+
+## 5. Usage and Interpretation
+
+- **Trend Identification:** The slope of the middle line indicates the direction of the trend.
+- **Dynamic Support and Resistance:** The channel lines act as dynamic support and resistance levels.
+- **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.
+- **Caution:** The indicator is "repainting" by nature. It is best used for confirming the current market structure rather than for generating precise entry signals from past data.