Linear Regression Intercept (LINEARREG_INTERCEPT)

The Linear Regression Intercept (LINEARREG_INTERCEPT) calculates the Y-intercept (b) of a linear regression line fitted over a specified period. This represents the starting point where the regression trendline crosses the Y-axis, providing the base level from which the trend begins. Combined with the slope, it allows complete reconstruction of the linear regression trendline for price projections and support/resistance identification.

What It Measures

LINEARREG_INTERCEPT measures: - Y-axis Starting Point: The value where the regression line intersects the Y-axis (when X=0) - Base Level: The theoretical price at the beginning of the regression period - Trendline Foundation: Essential component for constructing the complete trendline equation - Support/Resistance Levels: Historical intercept values can indicate potential price levels

The linear regression line equation is: Price = Intercept + (Slope × Time)

Usage

require 'sqa/tai'

prices = [45.50, 46.20, 46.80, 47.10, 47.50,
          48.00, 48.30, 48.70, 49.10, 49.50,
          50.00, 50.40, 50.80, 51.20, 51.60]

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

puts "Current Intercept: #{intercept.last.round(2)}"

Parameters

Parameter	Type	Required	Default	Description
prices	Array	Yes	-	Array of price values (typically closing prices)
period	Integer	No	14	Lookback period for regression calculation

Returns

Returns an array of intercept values. The first period - 1 values will be nil since insufficient data exists for calculation.

Interpretation

Intercept Behavior	Market Interpretation
Rising Intercept	Upward shift in base price level, bullish foundation
Falling Intercept	Downward shift in base price level, bearish foundation
Stable Intercept	Consistent base level, sideways trend foundation
High vs Price	Price trading below trendline, potential support
Low vs Price	Price trading above trendline, potential resistance

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

Key Concepts

1. Trendline Construction: Intercept + Slope define the complete trendline
2. Base Level Shift: Changes in intercept show shifts in trend foundation
3. Support/Resistance: Historical intercepts mark significant price levels
4. Price Projection: Use with slope to forecast future price levels

Example: Complete Trendline Construction

prices = [100.00, 101.50, 102.00, 103.50, 104.00,
          105.50, 106.00, 107.50, 108.00, 109.50,
          110.00, 111.50, 112.00, 113.50, 114.00]

period = 14

# Get all three regression components
intercept = SQA::TAI.linearreg_intercept(prices, period: period)
slope = SQA::TAI.linearreg_slope(prices, period: period)
regression_line = SQA::TAI.linearreg(prices, period: period)

current_intercept = intercept.last
current_slope = slope.last
current_regression = regression_line.last

puts <<~TRENDLINE
  === Complete Trendline Analysis ===
  Intercept (b): #{current_intercept.round(2)}
  Slope (m): #{current_slope.round(4)}
  Current Regression Value: #{current_regression.round(2)}

  Trendline Equation: Price = #{current_intercept.round(2)} + (#{current_slope.round(4)} × Time)

  Price Projections:
  - Next period: #{(current_intercept + (current_slope * period)).round(2)}
  - 2 periods ahead: #{(current_intercept + (current_slope * (period + 1))).round(2)}
  - 3 periods ahead: #{(current_intercept + (current_slope * (period + 2))).round(2)}
TRENDLINE

Example: Support/Resistance from Intercept

prices = load_historical_prices('AAPL')

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

# Track intercept levels for support/resistance
intercept_levels = intercept.compact.each_cons(5).map do |window|
  window.sum / window.size
end

current_price = prices.last
current_intercept = intercept.last

# Find nearby intercept levels
tolerance = current_price * 0.02  # 2% tolerance

nearby_levels = intercept_levels.select do |level|
  (level - current_price).abs <= tolerance
end

if nearby_levels.any?
  puts <<~SUPPORT_RESISTANCE
    === Support/Resistance Analysis ===
    Current Price: #{current_price.round(2)}
    Current Intercept: #{current_intercept.round(2)}

    Historical Intercept Levels Nearby:
  SUPPORT_RESISTANCE

  nearby_levels.each do |level|
    position = level < current_price ? "Support" : "Resistance"
    distance = ((level - current_price) / current_price * 100).round(2)
    puts "  #{position}: #{level.round(2)} (#{distance}%)"
  end
end

Example: Intercept Shift Detection

prices = load_historical_prices('TSLA')

period = 14
intercept = SQA::TAI.linearreg_intercept(prices, period: period)

# Calculate rate of change in intercept
intercept_changes = intercept.compact.each_cons(2).map do |prev, curr|
  ((curr - prev) / prev * 100).round(2)
end

recent_change = intercept_changes.last(5).sum / 5

if recent_change > 0.5
  puts <<~ANALYSIS
    === Intercept Rising ===
    Average Change: +#{recent_change.round(2)}%
    Interpretation: Base level shifting higher, bullish foundation
    Action: Look for uptrend continuation
  ANALYSIS
elsif recent_change < -0.5
  puts <<~ANALYSIS
    === Intercept Falling ===
    Average Change: #{recent_change.round(2)}%
    Interpretation: Base level shifting lower, bearish foundation
    Action: Consider defensive positioning
  ANALYSIS
else
  puts <<~ANALYSIS
    === Intercept Stable ===
    Average Change: #{recent_change.round(2)}%
    Interpretation: Consistent base level
    Action: Monitor for breakout
  ANALYSIS
end

Example: Trendline Channel Construction

prices = load_historical_prices('MSFT')
highs = load_historical_highs('MSFT')
lows = load_historical_lows('MSFT')

period = 14

# Calculate regression components for close, high, and low
intercept_close = SQA::TAI.linearreg_intercept(prices, period: period)
slope_close = SQA::TAI.linearreg_slope(prices, period: period)

intercept_high = SQA::TAI.linearreg_intercept(highs, period: period)
slope_high = SQA::TAI.linearreg_slope(highs, period: period)

intercept_low = SQA::TAI.linearreg_intercept(lows, period: period)
slope_low = SQA::TAI.linearreg_slope(lows, period: period)

# Construct channel
current_price = prices.last
current_time = period

# Calculate channel boundaries
upper_channel = intercept_high.last + (slope_high.last * current_time)
middle_line = intercept_close.last + (slope_close.last * current_time)
lower_channel = intercept_low.last + (slope_low.last * current_time)

channel_width = upper_channel - lower_channel
price_position = ((current_price - lower_channel) / channel_width * 100).round(2)

puts <<~CHANNEL
  === Regression Channel ===
  Upper Channel: #{upper_channel.round(2)}
  Middle Line: #{middle_line.round(2)}
  Lower Channel: #{lower_channel.round(2)}

  Channel Width: #{channel_width.round(2)}
  Current Price: #{current_price.round(2)}
  Position in Channel: #{price_position}%

  Trading Signals:
CHANNEL

if price_position > 80
  puts "  - Price near upper channel: Consider taking profits"
elsif price_position < 20
  puts "  - Price near lower channel: Consider buying opportunity"
else
  puts "  - Price in middle range: Wait for better entry"
end

Example: Multi-Period Intercept Analysis

prices = load_historical_prices('SPY')

periods = [10, 20, 50]

puts "=== Multi-Period Intercept Analysis ==="

periods.each do |period|
  intercept = SQA::TAI.linearreg_intercept(prices, period: period)
  slope = SQA::TAI.linearreg_slope(prices, period: period)

  current_intercept = intercept.last
  current_slope = slope.last

  # Project current value
  projected_value = current_intercept + (current_slope * period)
  current_price = prices.last

  deviation = ((current_price - projected_value) / projected_value * 100).round(2)

  puts <<~PERIOD_ANALYSIS

    #{period}-Period Analysis:
      Intercept: #{current_intercept.round(2)}
      Slope: #{current_slope.round(4)}
      Projected Value: #{projected_value.round(2)}
      Current Price: #{current_price.round(2)}
      Deviation: #{deviation}%
  PERIOD_ANALYSIS
end

# Analyze trend consistency
intercepts = periods.map do |period|
  SQA::TAI.linearreg_intercept(prices, period: period).last
end

if intercepts.sort == intercepts
  puts "\nAll intercepts rising: Strong uptrend structure"
elsif intercepts.sort.reverse == intercepts
  puts "\nAll intercepts falling: Strong downtrend structure"
else
  puts "\nMixed intercept levels: Trend inconsistency"
end

Example: Intercept with Angle for Trend Strength

prices = load_historical_prices('GOOGL')

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

current_intercept = intercept.last
current_slope = slope.last
current_angle = angle.last

# Calculate base level change
prev_intercept = intercept[-5]
intercept_change = ((current_intercept - prev_intercept) / prev_intercept * 100).round(2)

puts <<~TREND_STRENGTH
  === Trend Strength Analysis ===
  Base Level (Intercept): #{current_intercept.round(2)}
  Intercept Change (5 periods): #{intercept_change}%

  Trend Slope: #{current_slope.round(4)}
  Trend Angle: #{current_angle.round(2)}°

  Interpretation:
TREND_STRENGTH

case
when current_angle > 45
  puts "  - Very steep uptrend (#{current_angle.round(0)}°)"
  puts "  - Intercept shift: #{intercept_change}%"
  puts "  - Action: Caution on parabolic move, consider profit-taking"
when current_angle > 20
  puts "  - Strong uptrend (#{current_angle.round(0)}°)"
  puts "  - Intercept shift: #{intercept_change}%"
  puts "  - Action: Hold positions, trend is healthy"
when current_angle > 0
  puts "  - Mild uptrend (#{current_angle.round(0)}°)"
  puts "  - Intercept shift: #{intercept_change}%"
  puts "  - Action: Monitor for acceleration"
when current_angle > -20
  puts "  - Mild downtrend (#{current_angle.round(0)}°)"
  puts "  - Intercept shift: #{intercept_change}%"
  puts "  - Action: Consider defensive measures"
when current_angle > -45
  puts "  - Strong downtrend (#{current_angle.round(0)}°)"
  puts "  - Intercept shift: #{intercept_change}%"
  puts "  - Action: Avoid long positions"
else
  puts "  - Very steep downtrend (#{current_angle.round(0)}°)"
  puts "  - Intercept shift: #{intercept_change}%"
  puts "  - Action: Stay in cash or short"
end

Advanced Techniques

1. Trendline Equation Construction

Combine intercept with slope to create complete trendline equations: - y = intercept + (slope × x) - Use for precise price projections - Calculate expected price at any future period

2. Historical Support/Resistance

• Track historical intercept values
• Previous intercepts often act as support/resistance
• Create a map of significant price levels

3. Channel Analysis

• Calculate intercepts for high, low, and close prices
• Construct regression channels
• Identify overbought/oversold conditions within channel

4. Intercept Divergence

• Compare intercept direction with price direction
• Rising intercepts + falling prices = potential reversal
• Falling intercepts + rising prices = unsustainable rally

5. Multi-Timeframe Intercepts

• Calculate intercepts across multiple periods
• Aligned intercepts confirm trend strength
• Diverging intercepts signal trend weakness

Common Settings

Period	Use Case	Intercept Sensitivity
9-10	Short-term trading	High - rapid base level changes
14	Standard analysis	Medium - balanced responsiveness
20-21	Medium-term trends	Lower - smoother base levels
50	Long-term analysis	Low - major structural changes only
100+	Macro trends	Very low - fundamental shifts

Trading Applications

Entry Signals

• Price returns to projected trendline (intercept + slope × time)
• Intercept shifts upward after downtrend
• Price finds support at historical intercept level

Exit Signals

• Price diverges significantly from trendline
• Intercept begins declining during uptrend
• Price breaks through multiple historical intercept levels

Risk Management

• Use channel width (based on intercepts of high/low) for stop placement
• Monitor intercept stability for trend confidence
• Adjust position size based on intercept change rate

Limitations and Considerations

1. Linear Assumption: Assumes linear relationships, may miss curved trends
2. Historical Focus: Based on past data, doesn't predict external shocks
3. Period Sensitivity: Different periods yield different intercepts
4. Component Indicator: Most useful when combined with slope and angle
5. Not a Standalone Signal: Requires confirmation from other indicators

Related Indicators

• LINEARREG - Complete linear regression line
• LINEARREG_SLOPE - Slope of regression line
• LINEARREG_ANGLE - Angle of regression line
• TSF - Time Series Forecast
• STDDEV - Standard deviation for channel bands

See Also

• Back to Indicators
• Statistical Indicators Overview
• Basic Usage