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In statistics, linear regression is a linear approach for modelling the relationship between a scalar dependent variable y and one or more explanatory variables denoted X. The case of one explanatory variable is called simple linear regression. Wikipedia
Linear Regression Channel (LRC) is a very useful tool in trend analysis, especially for long term trend.
This Linear Regression Channel Pro version (LRC Pro) indicator has the following features:
It works on the following bar types:

If you used the Linear Regression Channel indicator before, you must know that the trend lines are not fixed. That trend is determined by calculating a Linear Regression Trend line using the least squares method.
With different 'Period' input value, the Linear Regression Trend lines vary greatly, let see an example of how LRC changes over time.
The chart below is taken from 1/26 with 'Period' =275, the Close price is above the 3rd upper trend line.
The chart below is taken from 2/5 with 'Period' =150, the Close price on 1/26 is still above the 3rd upper trend line, but the three Highs before 1/26 are within the trend line now.
The Low on 2/5 is below the 3rd lower trend line.

The chart below is taken from 2/5 with 'Period' =275, the Close price on 1/26 is still above the 3rd upper trend line, The Low on 2/5 is above the 3rd lower trendline.
The images below are random screenshots.
You can also use more than one instance with different inputs.
The Linear Regression Channel is a sophisticated statistical tool that moves beyond simple trend lines to provide a dynamic and objective view of the trend, its strength, and potential reversal points. Its usefulness in trading is profound because it doesn't just show where price is, but where it should be based on its statistical average, and then identifies when it becomes statistically extended or "overdone."
Here’s a detailed breakdown of why this indicator is so valuable.
The core of the indicator is the Linear Regression Line, which is the "line of best fit" through the chosen data points.
What it does: This central line represents the fair value or mean price over the selected period (e.g., 180 days). It objectively shows the true direction and slope of the trend, filtering out market noise.
Why it's useful:
Trend Direction: If the line is sloping up, the trend is objectively up. If it's sloping down, the trend is down. This removes emotional bias from trend identification.
Trend Strength: The steepness of the slope directly indicates the strength of the trend. A steep slope indicates a powerful, impulsive trend.
The channel's upper and lower bounds are not arbitrary; they are standard deviation or Fibonacci-based bands that represent volatility.
What it does: The channel is drawn at a certain distance (e.g., 1.618 standard deviations) from the central regression line. Your indicator uses Fibonacci multiples (1.618, 2.618), which are common volatility expansion multipliers.
Why it's useful:
The upper channel line acts as dynamic resistance in an uptrend.
The lower channel line acts as dynamic support in a downtrend.
Because the channel is based on volatility, it widens during volatile periods and narrows during quiet periods, giving a realistic view of the market environment.
This is where the indicator truly shines, offering strategies for both types of traders.
Mean Reversion (Reversion to the Mean): Price has a strong statistical tendency to return to its mean (the central regression line). This creates two high-probability setups:
Buying Dips: In a strong uptrend, price will often dip to or slightly below the central regression line, offering a high-probability long entry with a target back to the upper channel.
Selling Rips: In a strong downtrend, price will often rally to or slightly above the central regression line, offering a high-probability short entry.
Momentum / Trend Following (Extension Plays): A strong trend is characterized by price riding along one of the channel boundaries.
If price is consistently pushing the upper band in an uptrend, it signals powerful buying pressure.
A break outside the channel often indicates an extremely strong, possibly parabolic, move. However, it also signals that the move is statistically extended and may be due for a pullback to the mean.
The interaction with the channel's extremes can warn of an impending trend change.
What it shows: If price makes a new high or low outside the channel but then closes back inside, it is called a "channel rejection." This is often a strong sign that the momentum has exhausted itself.
Why it's useful: This can be an early warning sign to take profits on trend-following positions or even to prepare for a reversal trade. A break of the central regression line after such a rejection often confirms the trend shift.
Trend Identification: The Linear Regression line is sloping upward. The trend is objectively bullish.
Mean Reversion Entry: price pulls back from the upper channel. It falls and touches the central regression line. You see a bullish hammer candlestick form on the daily chart. This is your signal to enter a long position.
Risk Management: You place a stop-loss order just below the central line or the recent swing low.
Profit Target: Your initial profit target is a move back to the upper channel line (the 1.618 standard deviation level).
Momentum Scenario: Instead of pulling back, price rallies and pushes above the upper channel line (the 2.618 level). This confirms a very strong bullish impulse. You might hold your long position but be aware that the market is becoming extended.
Lagging Nature: Like all regression-based tools, it is lagging. It is based on past data. The channel redraws with each new bar.
Best in Trending Markets: It is most effective in clearly defined trending markets. It will give whipsaw signals in choppy, sideways (ranging) markets.
Channel Width is Key: The Fibonacci-based width in your indicator (1.618, 2.618) is excellent. If the channel is too narrow, you'll get false breaks. If it's too wide, the signals will be late. The Fibonacci multiples help adapt to volatility.
Confluence is King: Use this in conjunction with other indicators. For example, if price touches the central regression line and the 50-day simple moving average and a key Fibonacci retracement level, the probability of a bounce is much higher.
In essence, the Linear Regression Channel is useful because it:
Objectively Defines Trend: Provides a statistical, non-subjective measure of trend direction and strength.
Maps Volatility: The channel's width adapts to market volatility, providing realistic dynamic support and resistance.
Offers Two Strategies: Provides high-probability setups for both mean reversion traders (playing the pullbacks) and momentum traders (riding the channel boundaries).
Warns of Exhaustion: Signals when a trend is statistically extended and may be due for a reversal.
It is the ultimate tool for the trader who wants to move beyond simple lines and understand the underlying statistical reality of the market's trend. The "Auto" feature, as shown in your file, is crucial as it removes the subjectivity of manually drawing trend channels.
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