// The MIT License (MIT)
// © mihakralj
//@version=6
indicator("Regression Channels (REGCHANNEL)", "REGCHANNEL", overlay=true)

//@function Calculates Regression Channels with parallel lines equidistant from a central linear regression line
//@param period Lookback period for regression calculation (period > 1)
//@param source Source series for regression calculation (usually close)
//@param multiplier Distance multiplier for channel bands (multiplier > 0)
//@returns Tuple containing [upper_band, regression_line, lower_band]
//@optimized Uses linear regression with O(n) complexity per bar
regchannel(simple int period, series float source = close, simple float multiplier = 2.0) =>
    if period <= 1
        runtime.error("Period must be > 1")
    if multiplier <= 0.0
        runtime.error("Multiplier must be > 0")
    float sumX = 0.0
    float sumY = 0.0
    float sumXY = 0.0
    float sumX2 = 0.0
    for i = 0 to period - 1
        float x = float(i)
        float y = source[period - 1 - i]
        sumX := sumX + x
        sumY := sumY + y
        sumXY := sumXY + x * y
        sumX2 := sumX2 + x * x
    float n = float(period)
    float slope = (n * sumXY - sumX * sumY) / (n * sumX2 - sumX * sumX)
    float intercept = (sumY - slope * sumX) / n
    float currentX = float(period - 1)
    float regression = slope * currentX + intercept
    float sumResiduals2 = 0.0
    for i = 0 to period - 1
        float x = float(i)
        float y = source[period - 1 - i]
        float predicted = slope * x + intercept
        float residual = y - predicted
        sumResiduals2 := sumResiduals2 + residual * residual
    float stdDev = math.sqrt(sumResiduals2 / n)
    float upperBand = regression + multiplier * stdDev
    float lowerBand = regression - multiplier * stdDev
    [upperBand, regression, lowerBand]

// ---------- Main loop ----------

// Inputs
i_period = input.int(20, "Period", minval=2)
i_source = input.source(close, "Source")
i_multiplier = input.float(2.0, "Standard Deviation Multiplier", minval=0.1, step=0.1)

// Calculation
[upperBand, midLine, lowerBand] = regchannel(i_period, i_source, i_multiplier)

// Plot
p1 = plot(upperBand, "Upper Band", color=color.yellow, linewidth=2)
p2 = plot(midLine, "Regression Line", color=color.yellow, linewidth=2)
p3 = plot(lowerBand, "Lower Band", color=color.yellow, linewidth=2)
fill(p1, p2, color=color.new(color.red, 90), title="Upper Fill")
fill(p2, p3, color=color.new(color.green, 90), title="Lower Fill")