Linear Regression

20 periods is a good starting point for daily charts. Shorter periods (14) are more responsive but noisier. Longer periods (50) are smoother but slower to react. Match period to your trading timeframe - shorter for active trading, longer for position trading.

LR finds the best-fit line mathematically (least squares), while MAs simply average prices. LR has less lag than equivalent MAs. LR provides R² to measure trend validity. LR can be projected forward. Both show trend, but LR is more statistically rigorous.

Low R² (below 0.5-0.65) means prices aren't following a linear pattern - there's no clear straight-line trend. The LR line doesn't fit well. Don't use LR for trend trading when R² is low. Wait for R² to improve or use different methods.

Channel touches can be trading opportunities. In an uptrend (positive slope, high R²), touches of the LOWER channel are potential buy signals (mean reversion). Upper channel touches in downtrends are potential sells. Always confirm R² is adequate first.

LR can be mathematically extended forward (projection), but this assumes the current trend continues. Accuracy decreases rapidly beyond a few bars. Use projections for target estimation and scenario planning, not as predictions. Markets can change direction anytime.

Use short (14), medium (30), and long (50) period LR simultaneously. When all slopes align (all positive or all negative), trend is strong. Divergence (short turning while long still trending) warns of potential change. Use long LR for bias, short for timing.

2 standard deviations is standard, capturing ~95% of price action. Use 1.5 SD for more signals (tighter stops). Use 2.5 SD for fewer signals (wider stops). Match to your trading style - more aggressive = tighter channels.

LR provides trend context (slope, R²), RSI provides momentum. In uptrend (positive slope, high R²), buy when price at lower channel AND RSI oversold (<35). This combines statistical support with momentum exhaustion for higher probability entries.

Channel width is based on standard deviation of price from the LR line. As volatility changes, so does channel width. Wide channels = high volatility. Narrow channels = low volatility. This dynamic adjustment is a feature, not a bug.

Watch for: 1) R² declining (trend losing linearity), 2) Slope decreasing toward zero, 3) Price breaking below lower channel in uptrend, 4) Multi-period LR divergence (short turning while long still trending). Multiple warnings = higher probability of trend change.

Calculate R² for multiple periods (14, 20, 30, 50). Use the period with highest R² for current analysis. Alternatively, when R² is high (>0.8), extend period to capture more trend. When R² falls (<0.6), shorten period for responsiveness. Recalculate daily.

Residuals = Actual Price - LR Value at each point. Plot as oscillator. Extreme residuals (>2 SD) indicate price extended from trend - mean reversion likely. Use for entry timing: enter trend direction when residuals normalize from extremes.

Use LR channel boundaries for strike placement. Lower channel = put spread short strikes (support). Upper channel = call spread short strikes (resistance). LR line projection = target strikes. Channel width guides spread width. R² determines strategy confidence.

Track rolling profit factor by R² category and signal type. If high-R² lower channel entries show declining PF despite normal markets, edge may be decaying. Compare to simple buy-and-hold. If LR loses relative advantage, recalibrate parameters or pause system.

Testing shows R² > 0.75 dramatically improves results (71% WR, PF 3.15) versus R² 0.65-0.75 (60% WR, PF 2.35). Minimum threshold 0.65. For highest quality, wait for R² > 0.75, accepting fewer signals for higher win rate.