Linear Regression explained

Statistics

What Linear Regression measures

Linear Regression fits a straight line to price data over a lookback period using least-squares methodology, showing the 'equilibrium' price based on recent data. The LinReg line moves faster than a moving average and is less prone to lag. It identifies overbought/oversold conditions relative to the statistical mean and can predict where price 'should' be.

How Linear Regression readings are interpreted

Price above the LinReg line = trading above statistical fair value. Price below = below fair value. The slope of the line indicates trend direction and strength. Mean reversion to the LinReg line is a common setup — price stretched far from the line tends to return. LinReg channels (line ± standard error) define a normal trading range.

Conventional Linear Regression levels

Price > 2 standard errors above LinReg: statistically overbought
Price > 2 standard errors below LinReg: statistically oversold
LinReg slope positive and rising: accelerating uptrend
LinReg slope negative and steepening: accelerating downtrend
Price crossing LinReg: potential mean reversion or trend change

Where Linear Regression works, and where it does not

Most effective in smoothly trending or ranging markets. In erratic/gap-heavy markets, the statistical fit is poor and LinReg less meaningful. Works well for academic traders who prefer a statistical approach to overbought/oversold conditions.

Indicators commonly read alongside Linear Regression

Bollinger Bands: Both provide statistically-derived range — use LinReg when trend is present, BB when ranging
ATR: LinReg deviation + ATR multiple for stop placement
RSI: Price 2σ below LinReg + RSI oversold = strong mean-reversion buy

Known limitations of Linear Regression

LinReg recalculates the entire line when new bars are added — can look different in real-time vs backtesting
Shorter periods (5-10) make it too responsive; longer (50+) make it too slow
Not as widely known/used as SMA/EMA — less self-fulfilling

Linear Regression in practice

Slope direction is commonly used as a trend filter, with bullish readings treated as valid only while the slope is positive
In mean-reversion approaches, price 1.5–2 standard errors below a rising regression line is read as stretched, with the line itself as the reference target
The line is likewise the conventional reference for closing such a deviation once price returns to it
Weekly slope direction paired with daily RSI is a standard combination for separating direction from timing

Other statistical measures

Z-Score
Standard Deviation
Kurtosis
Skewness

Testing ideas built on Linear Regression

A reading of Linear Regression can be written as an exact rule and checked against historical data — as a full strategy with entries, exits and costs, or as a single condition and what followed it:

How to backtest a trading strategy without code
Event analysis: what follows a market event

Plot it yourself. Add this indicator to a chart, change every parameter and watch the line move, then backtest how the rule would have behaved on historical data — free on the S&P 500 ETF, no card.

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This is reference material, not advice. It describes what each indicator measures and how its readings are conventionally interpreted. Nothing here is a recommendation to buy or sell anything, and no indicator predicts future prices. GU Analyser is an analytical tool — no money is ever traded here.