Linear Regression Slope (LINEARREG_SLOPE)

The Linear Regression Slope indicator measures the slope (rate of change) of the linear regression line over a specified period. It quantifies the speed and direction of price movement, making it an excellent tool for identifying trend strength, momentum, and potential trend reversals.

What It Measures

LINEARREG_SLOPE calculates the slope coefficient (rise over run) of the best-fit linear regression line through price data. The slope value represents:

• Rate of Change: Points gained or lost per period
• Trend Direction: Positive (uptrend) or negative (downtrend)
• Trend Strength: Larger absolute values indicate stronger trends
• Momentum: Changes in slope indicate acceleration or deceleration

Usage

require 'sqa/tai'

prices = [100.0, 102.5, 104.0, 103.5, 105.0, 107.5,
          109.0, 108.5, 110.0, 112.0, 113.5, 115.0,
          114.5, 116.0, 118.5, 120.0, 119.5, 121.0]

# Calculate 14-period linear regression slope
slope = SQA::TAI.linearreg_slope(prices, period: 14)

puts "Current slope: #{slope.last.round(4)}"
puts "Trend: #{slope.last > 0 ? 'Uptrend' : 'Downtrend'}"
puts "Strength: #{slope.last.abs.round(4)} points/period"

Parameters

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

Returns

Returns an array of slope values representing the rate of price change per period. The first period - 1 values will be nil. Slope values can be positive (uptrend), negative (downtrend), or near zero (sideways).

Interpretation

Slope Value	Interpretation
> 1.0	Strong uptrend - rapid price increase
0.1 to 1.0	Moderate uptrend - steady price increase
-0.1 to 0.1	Sideways/neutral - no clear trend
-1.0 to -0.1	Moderate downtrend - steady price decrease
< -1.0	Strong downtrend - rapid price decrease

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

Key Signals

1. Slope Direction:
2. Positive slope: Prices trending upward
3. Negative slope: Prices trending downward

4. Zero slope: Prices moving sideways

5. Slope Magnitude:

6. Large absolute value: Strong, consistent trend
7. Small absolute value: Weak or choppy trend
8. Increasing magnitude: Trend acceleration

9. Decreasing magnitude: Trend deceleration

10. Slope Changes:

11. Slope crosses from negative to positive: Potential bullish reversal
12. Slope crosses from positive to negative: Potential bearish reversal
13. Slope diverges from price: Potential trend exhaustion

Example: Basic Slope Trading

prices = load_historical_prices('AAPL')

slope = SQA::TAI.linearreg_slope(prices, period: 14)
current_slope = slope.last

# Trend identification and strength
if current_slope > 0.5
  puts "Strong uptrend detected"
  puts "Slope: +#{current_slope.round(4)} points/period"
  puts "Signal: HOLD longs or BUY on pullbacks"
elsif current_slope > 0
  puts "Weak uptrend detected"
  puts "Slope: +#{current_slope.round(4)} points/period"
  puts "Signal: Monitor for strengthening or reversal"
elsif current_slope < -0.5
  puts "Strong downtrend detected"
  puts "Slope: #{current_slope.round(4)} points/period"
  puts "Signal: HOLD shorts or SELL on rallies"
elsif current_slope < 0
  puts "Weak downtrend detected"
  puts "Slope: #{current_slope.round(4)} points/period"
  puts "Signal: Monitor for strengthening or reversal"
else
  puts "Sideways/neutral trend"
  puts "Slope: #{current_slope.round(4)} points/period"
  puts "Signal: Wait for trend development"
end

Example: Slope Reversal Detection

prices = load_historical_prices('TSLA')

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

# Check for slope reversals
previous_slope = slope[-2]
current_slope = slope.last

if previous_slope.nil? || current_slope.nil?
  puts "Insufficient data"
else
  # Bullish reversal: slope crosses from negative to positive
  if previous_slope < 0 && current_slope > 0
    puts "BULLISH REVERSAL SIGNAL"
    puts "Slope changed from #{previous_slope.round(4)} to #{current_slope.round(4)}"
    puts "Action: Consider LONG entry"
    puts "Strength: #{current_slope > 0.5 ? 'Strong' : 'Weak'}"

  # Bearish reversal: slope crosses from positive to negative
  elsif previous_slope > 0 && current_slope < 0
    puts "BEARISH REVERSAL SIGNAL"
    puts "Slope changed from #{previous_slope.round(4)} to #{current_slope.round(4)}"
    puts "Action: Consider SHORT entry or exit longs"
    puts "Strength: #{current_slope < -0.5 ? 'Strong' : 'Weak'}"

  # Trend acceleration
  elsif current_slope.abs > previous_slope.abs * 1.5
    trend_direction = current_slope > 0 ? "upward" : "downward"
    puts "TREND ACCELERATION"
    puts "#{trend_direction.capitalize} trend is accelerating"
    puts "Slope: #{previous_slope.round(4)} -> #{current_slope.round(4)}"

  # Trend deceleration
  elsif current_slope.abs < previous_slope.abs * 0.5
    trend_direction = current_slope > 0 ? "upward" : "downward"
    puts "TREND DECELERATION WARNING"
    puts "#{trend_direction.capitalize} trend is losing momentum"
    puts "Slope: #{previous_slope.round(4)} -> #{current_slope.round(4)}"
  end
end

Example: Slope Divergence Strategy

prices = load_historical_prices('NVDA')

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

# Compare recent highs/lows
price_high_1 = prices[-20..-11].max
price_high_2 = prices[-10..-1].max

slope_high_1 = slope[-20..-11].compact.max
slope_high_2 = slope[-10..-1].compact.max

# Bearish divergence: price makes higher high, slope makes lower high
if price_high_2 > price_high_1 && slope_high_2 < slope_high_1
  puts "BEARISH DIVERGENCE DETECTED"
  puts "Price higher high: #{price_high_1} -> #{price_high_2}"
  puts "Slope lower high: #{slope_high_1.round(4)} -> #{slope_high_2.round(4)}"
  puts "Signal: Uptrend losing momentum - potential reversal"
  puts "Action: Consider taking profits or preparing for short"
end

# Check for bullish divergence
price_low_1 = prices[-20..-11].min
price_low_2 = prices[-10..-1].min

slope_low_1 = slope[-20..-11].compact.min
slope_low_2 = slope[-10..-1].compact.min

# Bullish divergence: price makes lower low, slope makes higher low
if price_low_2 < price_low_1 && slope_low_2 > slope_low_1
  puts "BULLISH DIVERGENCE DETECTED"
  puts "Price lower low: #{price_low_1} -> #{price_low_2}"
  puts "Slope higher low: #{slope_low_1.round(4)} -> #{slope_low_2.round(4)}"
  puts "Signal: Downtrend losing momentum - potential reversal"
  puts "Action: Consider bottom fishing or preparing for long"
end

Example: Slope with Trend Filter

prices = load_historical_prices('MSFT')

slope = SQA::TAI.linearreg_slope(prices, period: 14)
sma_50 = SQA::TAI.sma(prices, period: 50)
sma_200 = SQA::TAI.sma(prices, period: 200)

current_price = prices.last
current_slope = slope.last

# Determine overall trend
trend = if sma_50.last > sma_200.last
  "uptrend"
elsif sma_50.last < sma_200.last
  "downtrend"
else
  "sideways"
end

puts "Overall trend: #{trend.upcase}"
puts "Current slope: #{current_slope.round(4)}"

# Trading signals aligned with trend
case trend
when "uptrend"
  if current_slope > 0.5
    puts "Strong uptrend confirmed by slope"
    puts "Signal: STRONG BUY - trend acceleration"
  elsif current_slope > 0
    puts "Uptrend intact but weakening"
    puts "Signal: HOLD or add on dips"
  elsif current_slope < 0
    puts "WARNING: Negative slope in uptrend"
    puts "Signal: Possible pullback - wait for confirmation"
  end

when "downtrend"
  if current_slope < -0.5
    puts "Strong downtrend confirmed by slope"
    puts "Signal: STRONG SELL or SHORT"
  elsif current_slope < 0
    puts "Downtrend intact but weakening"
    puts "Signal: HOLD shorts or add on rallies"
  elsif current_slope > 0
    puts "WARNING: Positive slope in downtrend"
    puts "Signal: Possible bounce - wait for confirmation"
  end

when "sideways"
  if current_slope.abs < 0.1
    puts "Sideways trend confirmed by flat slope"
    puts "Signal: Range trading strategy"
  else
    puts "Slope developing: #{current_slope > 0 ? 'bullish' : 'bearish'}"
    puts "Signal: Potential breakout forming"
  end
end

Example: Slope Acceleration Signals

prices = load_historical_prices('AMZN')

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

# Calculate slope change rate (acceleration)
slope_changes = []
(1...slope.length).each do |i|
  next if slope[i].nil? || slope[i-1].nil?
  slope_changes << slope[i] - slope[i-1]
end

recent_acceleration = slope_changes.last(5).compact

if recent_acceleration.any?
  avg_acceleration = recent_acceleration.sum / recent_acceleration.length

  puts "Current slope: #{slope.last.round(4)}"
  puts "Average acceleration: #{avg_acceleration.round(6)}"

  if avg_acceleration > 0.1
    puts "STRONG ACCELERATION DETECTED"
    puts "Trend is gaining momentum rapidly"
    puts "Signal: Momentum trade opportunity"
    puts "Action: #{slope.last > 0 ? 'BUY breakout' : 'SELL breakdown'}"

  elsif avg_acceleration > 0.01
    puts "Moderate acceleration detected"
    puts "Trend is strengthening"
    puts "Signal: Trend following opportunity"

  elsif avg_acceleration < -0.1
    puts "STRONG DECELERATION DETECTED"
    puts "Trend is losing momentum rapidly"
    puts "Signal: Reversal warning"
    puts "Action: Prepare to exit or reverse position"

  elsif avg_acceleration < -0.01
    puts "Moderate deceleration detected"
    puts "Trend is weakening"
    puts "Signal: Take profits or tighten stops"

  else
    puts "Stable slope - consistent trend"
    puts "Signal: Maintain current strategy"
  end
end

Example: Multi-Period Slope Analysis

prices = load_historical_prices('GOOGL')

# Calculate slopes for different periods
slope_short = SQA::TAI.linearreg_slope(prices, period: 7)
slope_medium = SQA::TAI.linearreg_slope(prices, period: 14)
slope_long = SQA::TAI.linearreg_slope(prices, period: 28)

puts "Short-term slope (7): #{slope_short.last.round(4)}"
puts "Medium-term slope (14): #{slope_medium.last.round(4)}"
puts "Long-term slope (28): #{slope_long.last.round(4)}"

# Analyze slope alignment
all_positive = [slope_short.last, slope_medium.last, slope_long.last].all? { |s| s > 0 }
all_negative = [slope_short.last, slope_medium.last, slope_long.last].all? { |s| s < 0 }

if all_positive
  puts "\nALL SLOPES POSITIVE - Strong uptrend"

  if slope_short.last > slope_medium.last && slope_medium.last > slope_long.last
    puts "Accelerating uptrend - slopes increasing"
    puts "Signal: STRONG BUY - momentum building"
  else
    puts "Mixed slope magnitudes"
    puts "Signal: BUY but monitor for changes"
  end

elsif all_negative
  puts "\nALL SLOPES NEGATIVE - Strong downtrend"

  if slope_short.last < slope_medium.last && slope_medium.last < slope_long.last
    puts "Accelerating downtrend - slopes steepening"
    puts "Signal: STRONG SELL - momentum building"
  else
    puts "Mixed slope magnitudes"
    puts "Signal: SELL but monitor for changes"
  end

else
  puts "\nMIXED SLOPES - Conflicting signals"

  if slope_short.last > 0 && slope_medium.last < 0
    puts "Short-term reversal in downtrend"
    puts "Signal: Possible bottom forming"
  elsif slope_short.last < 0 && slope_medium.last > 0
    puts "Short-term reversal in uptrend"
    puts "Signal: Possible top forming"
  end
end

Advanced Techniques

1. Slope Bands

Create bands around zero slope to identify trend zones: - Strong trend: |slope| > 0.5 - Moderate trend: 0.1 < |slope| < 0.5 - Weak/sideways: |slope| < 0.1

2. Slope Rate of Change

Monitor how quickly the slope itself is changing to identify: - Trend acceleration (slope increasing) - Trend deceleration (slope decreasing) - Momentum exhaustion (slope rate flattening)

3. Slope Support/Resistance

Use historical slope levels as support/resistance: - Slopes often bounce at previous slope levels - Slope breakouts signal strong momentum shifts

4. Slope Histogram

Convert slope values to histogram format for visual clarity: - Positive bars: Uptrend strength - Negative bars: Downtrend strength - Bar height: Trend intensity

Example: Complete Slope Trading System

class SlopeTradingSystem
  def initialize(prices, short_period: 7, long_period: 21)
    @prices = prices
    @slope_short = SQA::TAI.linearreg_slope(prices, period: short_period)
    @slope_long = SQA::TAI.linearreg_slope(prices, period: long_period)
  end

  def analyze
    short = @slope_short.last
    long = @slope_long.last

    return nil if short.nil? || long.nil?

    # Calculate slope characteristics
    trend_strength = short.abs
    trend_direction = short > 0 ? "bullish" : "bearish"
    alignment = (short > 0 && long > 0) || (short < 0 && long < 0)

    # Generate signals
    signal = generate_signal(short, long, alignment)

    {
      short_slope: short.round(4),
      long_slope: long.round(4),
      trend_direction: trend_direction,
      trend_strength: classify_strength(trend_strength),
      alignment: alignment,
      signal: signal,
      confidence: calculate_confidence(short, long, alignment)
    }
  end

  private

  def generate_signal(short, long, alignment)
    if alignment && short > 0.5
      "STRONG BUY"
    elsif alignment && short > 0
      "BUY"
    elsif alignment && short < -0.5
      "STRONG SELL"
    elsif alignment && short < 0
      "SELL"
    elsif short > 0 && long < 0
      "BULLISH REVERSAL"
    elsif short < 0 && long > 0
      "BEARISH REVERSAL"
    else
      "NEUTRAL"
    end
  end

  def classify_strength(slope_abs)
    case slope_abs
    when 0...0.1 then "weak"
    when 0.1...0.5 then "moderate"
    when 0.5...1.0 then "strong"
    else "very strong"
    end
  end

  def calculate_confidence(short, long, alignment)
    base = alignment ? 0.7 : 0.3
    strength_bonus = [short.abs, 1.0].min * 0.3
    (base + strength_bonus).round(2)
  end
end

# Usage
prices = load_historical_prices('AAPL')
system = SlopeTradingSystem.new(prices)
result = system.analyze

puts <<~ANALYSIS
  === SLOPE TRADING ANALYSIS ===
  Short-term slope: #{result[:short_slope]}
  Long-term slope: #{result[:long_slope]}
  Trend direction: #{result[:trend_direction].upcase}
  Trend strength: #{result[:trend_strength].upcase}
  Slopes aligned: #{result[:alignment] ? 'YES' : 'NO'}

  SIGNAL: #{result[:signal]}
  Confidence: #{(result[:confidence] * 100).round(0)}%
ANALYSIS

Common Settings

Period	Use Case	Sensitivity
5-7	Very short-term trading	High - quick signals, more noise
10-14	Short-term trading (standard)	Moderate - balanced approach
20-25	Swing trading	Lower - smoother signals
50+	Position trading	Low - major trend changes only

Advantages

• Quantifies trend strength objectively
• Identifies trend acceleration/deceleration
• Easy to interpret (positive/negative/magnitude)
• Works well with other regression indicators
• Excellent for momentum trading
• Less lag than moving averages

Limitations

• Can be whipsawed in choppy markets
• Absolute slope values depend on price level
• No inherent overbought/oversold levels
• May give false signals in ranging markets
• Requires context (compare to historical slopes)

Tips for Use

1. Normalize slopes by dividing by price for cross-asset comparison
2. Use multiple periods to confirm trend across timeframes
3. Combine with price action to confirm slope signals
4. Monitor slope changes as much as slope values
5. Set thresholds based on historical slope distributions
6. Use divergences to identify potential reversals early

Related Indicators

• LINEARREG - Linear regression forecast value
• LINEARREG_ANGLE - Slope expressed as angle in degrees
• LINEARREG_INTERCEPT - Y-intercept of regression line
• TSF - Time Series Forecast (regression + projection)
• ROC - Rate of Change (similar concept)
• MOM - Momentum indicator

See Also

• Back to Indicators
• Statistical Indicators Overview
• Basic Usage
• Trend Following Strategies