Linear Regression Angle (LINEARREG_ANGLE)

The Linear Regression Angle indicator measures the angle of the linear regression line in degrees. It quantifies the steepness and direction of price trends, providing a numerical measure of trend strength. Values range from -90 to +90 degrees, where steeper angles indicate stronger trends.

Usage

require 'sqa/tai'

prices = [44.34, 44.09, 44.15, 43.61, 44.33, 44.83,
          45.10, 45.42, 45.84, 46.08, 46.03, 46.41,
          46.22, 45.64, 46.21, 46.25, 46.08, 46.46,
          46.57, 45.95, 46.50, 46.02, 46.55, 47.03]

# Calculate 14-period Linear Regression Angle
angle = SQA::TAI.linearreg_angle(prices, period: 14)

puts "Current angle: #{angle.last.round(2)} degrees"

Parameters

Parameter	Type	Required	Default	Description
prices	Array	Yes	-	Array of price values
period	Integer	No	14	Number of periods for linear regression calculation

Returns

Returns an array of angle values in degrees, ranging from -90 to +90. The first period - 1 values will be nil.

Interpretation

Angle Range	Trend Direction	Trend Strength	Interpretation
+45 to +90	Uptrend	Very Strong	Steep upward momentum - strong bull trend
+30 to +45	Uptrend	Strong	Sustained upward momentum
+15 to +30	Uptrend	Moderate	Gentle upward trend
+5 to +15	Uptrend	Weak	Slight upward bias
-5 to +5	Sideways	Neutral	Flat/consolidating market
-15 to -5	Downtrend	Weak	Slight downward bias
-30 to -15	Downtrend	Moderate	Gentle downward trend
-45 to -30	Downtrend	Strong	Sustained downward momentum
-90 to -45	Downtrend	Very Strong	Steep downward momentum - strong bear trend

Note: Array elements should be ordered from oldest to newest (chronological order)

Key Insights

• Positive angles: Indicate uptrends with steeper angles showing stronger upward momentum
• Negative angles: Indicate downtrends with steeper angles showing stronger downward momentum
• Near 0 degrees (-5 to +5): Market is moving sideways or consolidating
• 45-degree angle: Considered the benchmark for a strong, sustainable trend
• Above 60 degrees: Extremely steep trend, may be unsustainable
• Angle flattening: Momentum is weakening, potential trend exhaustion
• Angle steepening: Momentum is accelerating

Example: Basic Trend Strength Detection

prices = load_historical_prices('AAPL')

angle = SQA::TAI.linearreg_angle(prices, period: 14)
current_angle = angle.last

case current_angle
when 45..90
  puts "Very strong uptrend (#{current_angle.round(2)}°) - Strong BUY"
when 30...45
  puts "Strong uptrend (#{current_angle.round(2)}°) - BUY"
when 15...30
  puts "Moderate uptrend (#{current_angle.round(2)}°) - Bullish bias"
when -15...15
  puts "Sideways market (#{current_angle.round(2)}°) - No clear trend"
when -30...-15
  puts "Moderate downtrend (#{current_angle.round(2)}°) - Bearish bias"
when -45...-30
  puts "Strong downtrend (#{current_angle.round(2)}°) - SELL"
when -90...-45
  puts "Very strong downtrend (#{current_angle.round(2)}°) - Strong SELL"
end

Example: Trend Change Detection

prices = load_historical_prices('TSLA')

angle = SQA::TAI.linearreg_angle(prices, period: 14)

# Detect trend changes
previous_angle = angle[-2]
current_angle = angle[-1]

# Trend strengthening or weakening
if current_angle > previous_angle && current_angle > 0
  puts "Uptrend strengthening: #{previous_angle.round(2)}° -> #{current_angle.round(2)}°"
elsif current_angle < previous_angle && current_angle < 0
  puts "Downtrend strengthening: #{previous_angle.round(2)}° -> #{current_angle.round(2)}°"
elsif current_angle.abs < previous_angle.abs
  puts "Trend weakening: #{previous_angle.round(2)}° -> #{current_angle.round(2)}°"
end

# Trend reversal detection
if previous_angle > 20 && current_angle < 5
  puts "Uptrend losing momentum - potential reversal signal"
elsif previous_angle < -20 && current_angle > -5
  puts "Downtrend losing momentum - potential reversal signal"
end

# Direction change
if previous_angle > 0 && current_angle < 0
  puts "Trend changed from UP to DOWN"
elsif previous_angle < 0 && current_angle > 0
  puts "Trend changed from DOWN to UP"
end

Example: Angle-Based Entry and Exit Strategy

prices = load_historical_prices('MSFT')

angle = SQA::TAI.linearreg_angle(prices, period: 14)
slope = SQA::TAI.linearreg_slope(prices, period: 14)

current_angle = angle.last
previous_angle = angle[-2]

# Entry signals based on angle strength
if current_angle > 30 && previous_angle < 30
  puts "Entering LONG position - angle crossed above 30° threshold"
  puts "Strong uptrend confirmed at #{current_angle.round(2)}°"
elsif current_angle < -30 && previous_angle > -30
  puts "Entering SHORT position - angle crossed below -30° threshold"
  puts "Strong downtrend confirmed at #{current_angle.round(2)}°"
end

# Exit signals based on angle flattening
if current_angle > 0 && current_angle < 15 && previous_angle > 15
  puts "Exiting LONG - uptrend weakening (#{current_angle.round(2)}°)"
elsif current_angle < 0 && current_angle > -15 && previous_angle < -15
  puts "Exiting SHORT - downtrend weakening (#{current_angle.round(2)}°)"
end

# Warning signals
if current_angle > 70
  puts "WARNING: Extremely steep uptrend (#{current_angle.round(2)}°)"
  puts "May be unsustainable - consider taking profits"
elsif current_angle < -70
  puts "WARNING: Extremely steep downtrend (#{current_angle.round(2)}°)"
  puts "May be unsustainable - consider covering shorts"
end

Example: Multiple Period Analysis

prices = load_historical_prices('NVDA')

# Compare different timeframes
angle_short = SQA::TAI.linearreg_angle(prices, period: 10)
angle_medium = SQA::TAI.linearreg_angle(prices, period: 20)
angle_long = SQA::TAI.linearreg_angle(prices, period: 50)

puts "Short-term angle (10): #{angle_short.last.round(2)}°"
puts "Medium-term angle (20): #{angle_medium.last.round(2)}°"
puts "Long-term angle (50): #{angle_long.last.round(2)}°"

# All timeframes aligned
if angle_short.last > 30 && angle_medium.last > 25 && angle_long.last > 20
  puts "All timeframes showing strong uptrend - HIGH CONFIDENCE BUY"
elsif angle_short.last < -30 && angle_medium.last < -25 && angle_long.last < -20
  puts "All timeframes showing strong downtrend - HIGH CONFIDENCE SELL"
end

# Divergence between timeframes
if angle_short.last > 30 && angle_long.last < 0
  puts "Short-term bullish but long-term bearish - CAUTION"
elsif angle_short.last < -30 && angle_long.last > 0
  puts "Short-term bearish but long-term bullish - CAUTION"
end

Example: Combining with Linear Regression Slope

prices = load_historical_prices('GOOGL')

angle = SQA::TAI.linearreg_angle(prices, period: 14)
slope = SQA::TAI.linearreg_slope(prices, period: 14)
linreg = SQA::TAI.linearreg(prices, period: 14)

current_price = prices.last
current_angle = angle.last
current_slope = slope.last
current_linreg = linreg.last

puts "Current price: $#{current_price.round(2)}"
puts "Linear regression value: $#{current_linreg.round(2)}"
puts "Slope: #{current_slope.round(4)}"
puts "Angle: #{current_angle.round(2)}°"

# Strong trend confirmation
if current_angle > 45 && current_price > current_linreg
  puts "Strong uptrend with price above regression line - STRONG BUY"
  puts "Expected continuation of upward momentum"
elsif current_angle < -45 && current_price < current_linreg
  puts "Strong downtrend with price below regression line - STRONG SELL"
  puts "Expected continuation of downward momentum"
end

# Mean reversion opportunities
if current_angle.abs < 10 && (current_price - current_linreg).abs > (current_price * 0.02)
  if current_price < current_linreg
    puts "Price below regression line in sideways market - potential BUY"
  else
    puts "Price above regression line in sideways market - potential SELL"
  end
end

Example: Angle Histogram for Trend Analysis

prices = load_historical_prices('AAPL')

angle = SQA::TAI.linearreg_angle(prices, period: 14)

# Analyze recent angle history
recent_angles = angle.compact.last(20)

# Calculate statistics
avg_angle = recent_angles.sum / recent_angles.size
max_angle = recent_angles.max
min_angle = recent_angles.min

puts "Average angle (last 20): #{avg_angle.round(2)}°"
puts "Max angle: #{max_angle.round(2)}°"
puts "Min angle: #{min_angle.round(2)}°"
puts "Range: #{(max_angle - min_angle).round(2)}°"

# Trend consistency
if recent_angles.all? { |a| a > 20 }
  puts "Consistently strong uptrend"
elsif recent_angles.all? { |a| a < -20 }
  puts "Consistently strong downtrend"
elsif recent_angles.all? { |a| a.abs < 15 }
  puts "Consistently sideways/consolidating"
else
  puts "Mixed trend - no clear consistency"
end

# Volatility in angle
angle_std = Math.sqrt(recent_angles.map { |a| (a - avg_angle)**2 }.sum / recent_angles.size)
puts "Angle standard deviation: #{angle_std.round(2)}°"

if angle_std > 20
  puts "High angle volatility - unstable trend"
elsif angle_std < 5
  puts "Low angle volatility - stable trend"
end

Trading Strategies

1. Strong Trend Following

• Enter long when angle crosses above 30°
• Enter short when angle crosses below -30°
• Exit when angle flattens below 15° (long) or above -15° (short)
• Best for trending markets

2. Angle Momentum Strategy

• Buy when angle is rising and above 20°
• Sell when angle is falling and below -20°
• Hold positions as long as angle maintains direction
• Add to positions when angle steepens

3. Mean Reversion in Sideways Markets

• Trade only when angle is between -10° and +10°
• Buy when price is below regression line
• Sell when price is above regression line
• Exit when angle breaks out of range

4. Trend Exhaustion Detection

• Watch for angles above 60° or below -60°
• Reduce position size as angle becomes extreme
• Exit when angle starts to flatten
• Prepare for potential reversal

Common Period Settings

Period	Use Case	Sensitivity
7-10	Short-term trading	High - More responsive, more signals
14	Standard analysis	Medium - Balanced approach
20-25	Swing trading	Medium-Low - Smoother trends
50+	Long-term trends	Low - Very smooth, fewer signals

Angle Strength Guidelines

Uptrend Strength

• Weak (5-15°): Gentle rise, be cautious
• Moderate (15-30°): Steady uptrend, good for accumulation
• Strong (30-45°): Solid uptrend, ideal for trend following
• Very Strong (45-60°): Powerful uptrend, monitor for sustainability
• Extreme (60-90°): Parabolic move, high risk of reversal

Downtrend Strength

• Weak (-5 to -15°): Gentle decline, be cautious
• Moderate (-15 to -30°): Steady downtrend, consider shorts
• Strong (-30 to -45°): Solid downtrend, ideal for short selling
• Very Strong (-45 to -60°): Powerful downtrend, monitor for bounce
• Extreme (-60 to -90°): Capitulation, possible oversold

Advanced Techniques

1. Angle Divergence

Watch for divergence between price and angle: - Price making higher highs but angle decreasing = bearish divergence - Price making lower lows but angle increasing = bullish divergence

2. Angle Channels

Track the range of angles over time: - Consistent angle range indicates stable trend - Expanding angle range indicates increasing volatility - Contracting angle range indicates consolidation

3. Multi-Timeframe Angle Alignment

Strongest signals when angles align across timeframes: - Daily, weekly, monthly all positive = strong bull market - Daily, weekly, monthly all negative = strong bear market

Related Indicators

• LINEARREG_SLOPE - Raw slope value (not in degrees)
• LINEARREG - Linear regression line value
• LINEARREG_INTERCEPT - Y-intercept of regression line
• TSF - Time Series Forecast
• ADX - Trend strength (different method)

See Also

• Back to Indicators
• Statistical Indicators Overview
• Basic Usage