Linear Regression Indicator (LRI)
The Statistically Perfect 'Fair-Value' Trend Axis
Imagine drawing the single straight line that best fits the last N prices ā the one that minimizes the total squared error. That's exactly what the Linear Regression Indicator (LRI) does, then projects that line right onto the current bar. It becomes a rolling 'fair-value' centerline: prices above it are temporarily strong, below it are weak. Add channel bands (Ā± k standard deviations) and you have dynamic support/resistance. It's the mathematically clean way to see both trend direction (slope) and deviation from the mean ā no arbitrary smoothing, just pure least-squares goodness.
The Math ā Simple Yet Powerful
On one napkin:
- For N prices, time index x = 0 (oldest) to Nā1 (newest).
- Fit line: y = Ī± + Ī²x (Ī± = intercept, Ī² = slope).
- Current LRI value (at newest bar): LRI = Ī± + Ī²(Nā1).
- Standard error Ļ measures average deviation ā use for channel bands (Ā±1Ļ, Ā±2Ļ).
Every new bar drops the oldest price and recalculates ā the line rolls forward smoothly.
Most platforms plot the endpoint value; some also show full regression channel.
Reading the Line and Channels
What to watch:
- Positive steep slope: Strong uptrend ā bias long, lower channel as stop/support.
- Negative slope: Downtrend ā bias short, upper channel as resistance/stop.
- Slope near zero: Trend fading into range ā prepare mean-reversion tools.
- Price piercing +1Ļ then snapping back: Over-extension ā potential fade opportunity.
- Price hugging centerline: Equilibrium ā low conviction moves.
Slope changes fast (often within one bar of real shift), while the line itself lags about half the window.
Battle-Tested Trading Setups
Proven frameworks:
- Channel Pullback: In uptrend, buy test of lower 1Ļ band; stop below ā2Ļ; target upper band or 1.5R.
- Slope Filter: Only take MA crossovers or momentum signals when absolute slope exceeds threshold (e.g., annualized >5%).
- Slope Divergence: Price new high + falling slope ā exhaustion; confirm with RSI/MACD to short.
- Mean-Reversion Swing: When slope flat (< small Īµ), sell spikes to +1.5Ļ, buy dips to ā1.5Ļ.
Pair slope with volume or ADX ā strong slope + rising ADX = high-conviction trend.
The Wins and the Watch-Outs
Strengths
- Statistically optimal fit ā minimizes squared error.
- Gives both level (fair value) and velocity (slope).
- Foundation for channels, z-scores, and volatility stops.
- Clean, objective ā no arbitrary smoothing constants.
Limitations
- Equal weighting ā vulnerable to outliers; single freak bar tilts line.
- Built-in lag (~Ā½ N bars) on the value itself.
- Window sensitive ā too short = noisy, too long = sluggish.
- Assumes linear trend ā curved markets need shorter N or alternatives.
Your LRI Setup Checklist
- Choose N matching timeframe: 20ā50 swings, 100ā200 position trades.
- Decide channel width (Ā±1Ļ common for entries, Ā±2Ļ for stops).
- Backtest slope thresholds and pullback rules.
- Filter with momentum/volume ā avoid flat-slope traps.
- Consider robust variants or outlier clipping on wild assets.
Key Takeaways
LRI plots the rolling least-squares best-fit line ā your dynamic fair-value axis.
Slope shows trend velocity; channels give objective support/resistance.
Faster slope response than long averages, statistically clean fit.
Great for pullbacks, slope filters, divergences, and mean-reversion.
Tune N carefully, watch outliers, add confirmation ā and let the regression guide you to smarter trend and value plays. Stay fitted and trade sharp!
Linear Regression Indicator (LRI)
The Statistically Perfect 'Fair-Value' Trend Axis
Imagine drawing the single straight line that best fits the last N prices ā the one that minimizes the total squared error. That's exactly what the Linear Regression Indicator (LRI) does, then projects that line right onto the current bar. It becomes a rolling 'fair-value' centerline: prices above it are temporarily strong, below it are weak. Add channel bands (Ā± k standard deviations) and you have dynamic support/resistance. It's the mathematically clean way to see both trend direction (slope) and deviation from the mean ā no arbitrary smoothing, just pure least-squares goodness.
Table of Contents
The Math ā Simple Yet Powerful
On one napkin:
- For N prices, time index x = 0 (oldest) to Nā1 (newest).
- Fit line: y = Ī± + Ī²x (Ī± = intercept, Ī² = slope).
- Current LRI value (at newest bar): LRI = Ī± + Ī²(Nā1).
- Standard error Ļ measures average deviation ā use for channel bands (Ā±1Ļ, Ā±2Ļ).
Every new bar drops the oldest price and recalculates ā the line rolls forward smoothly.
Most platforms plot the endpoint value; some also show full regression channel.
Reading the Line and Channels
What to watch:
- Positive steep slope: Strong uptrend ā bias long, lower channel as stop/support.
- Negative slope: Downtrend ā bias short, upper channel as resistance/stop.
- Slope near zero: Trend fading into range ā prepare mean-reversion tools.
- Price piercing +1Ļ then snapping back: Over-extension ā potential fade opportunity.
- Price hugging centerline: Equilibrium ā low conviction moves.
Slope changes fast (often within one bar of real shift), while the line itself lags about half the window.
Battle-Tested Trading Setups
Proven frameworks:
- Channel Pullback: In uptrend, buy test of lower 1Ļ band; stop below ā2Ļ; target upper band or 1.5R.
- Slope Filter: Only take MA crossovers or momentum signals when absolute slope exceeds threshold (e.g., annualized >5%).
- Slope Divergence: Price new high + falling slope ā exhaustion; confirm with RSI/MACD to short.
- Mean-Reversion Swing: When slope flat (< small Īµ), sell spikes to +1.5Ļ, buy dips to ā1.5Ļ.
Pair slope with volume or ADX ā strong slope + rising ADX = high-conviction trend.
The Wins and the Watch-Outs
Strengths
- Statistically optimal fit ā minimizes squared error.
- Gives both level (fair value) and velocity (slope).
- Foundation for channels, z-scores, and volatility stops.
- Clean, objective ā no arbitrary smoothing constants.
Limitations
- Equal weighting ā vulnerable to outliers; single freak bar tilts line.
- Built-in lag (~Ā½ N bars) on the value itself.
- Window sensitive ā too short = noisy, too long = sluggish.
- Assumes linear trend ā curved markets need shorter N or alternatives.
Your LRI Setup Checklist
- Choose N matching timeframe: 20ā50 swings, 100ā200 position trades.
- Decide channel width (Ā±1Ļ common for entries, Ā±2Ļ for stops).
- Backtest slope thresholds and pullback rules.
- Filter with momentum/volume ā avoid flat-slope traps.
- Consider robust variants or outlier clipping on wild assets.
Key Takeaways
LRI plots the rolling least-squares best-fit line ā your dynamic fair-value axis.
Slope shows trend velocity; channels give objective support/resistance.
Faster slope response than long averages, statistically clean fit.
Great for pullbacks, slope filters, divergences, and mean-reversion.
Tune N carefully, watch outliers, add confirmation ā and let the regression guide you to smarter trend and value plays. Stay fitted and trade sharp!
Related Terms
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