Polynomial Regression Channel [ChartPrime]

⯁ OVERVIEW
The Polynomial Regression Channel [ChartPrime] fits price action using advanced polynomial regression, extending beyond simple linear or logarithmic models. By leveraging matrix calculations, it builds a curved regression line that adapts to swings more naturally. The channel includes extrapolated forward projections, helping traders visualize where price may gravitate in the near future. Midline color shifts reflect directional bias, while prediction ranges are marked with dashed extensions, labeled prices, and a live table for clarity.

⯁ KEY FEATURES

• Polynomial Regression Core:
  Uses matrix algebra to calculate a polynomial fit of customizable degree, adapting to complex, non-linear market structures.
  

  polyreg(source, length, degree, extrapolate) =>
      total = length + extrapolate
  
      X_all = matrix.new<float>(total, degree + 1, 0.0)
      for i = 0 to total - 1
          for j = 0 to degree
              matrix.set(X_all, i, j, math.pow(i, j))
  
      // y (length × 1), oldest→newest over the fit window
      y = matrix.new<float>(length, 1, 0.0)
      for i = 0 to length - 1
          matrix.set(y, i, 0, source[length - 1 - i])
  
      // X_train (first `length` rows of X_all)
      X_tr = matrix.new<float>(length, degree + 1, 0.0)
      for i = 0 to length - 1
          for j = 0 to degree
              matrix.set(X_tr, i, j, matrix.get(X_all, i, j))
  
      // OLS via normal equations: (X'X)^(-1)b = X'y  ⇒  b = (X'X)^(-1) X'y
      Xt   = matrix.transpose(X_tr)           // X'
      XtX  = matrix.mult(Xt, X_tr)           // (X'X) 
      Xty  = matrix.mult(Xt, y)             //  X'y
      XtX_inv = matrix.inv(XtX)            // (X'X)^(-1)      
      b       = matrix.mult(XtX_inv, Xty) //  b = (X'X)^(-1) X'y
  
      // Predictions for all rows (fit + extrap)
      preds = matrix.mult(X_all, matrix.col(b,0))    
      preds

• Extrapolated Future Projections:
  Forward-looking range (dashed lines + circular markers) shows where the fitted polynomial suggests price may move.
  
• Dynamic Midline Coloring:
  Regression midline shifts green when slope turns upward and magenta when slope turns downward, giving instant directional context.
  
• Channel Boundaries:
  Upper and lower levels expand from the midline using a volatility-based offset, framing potential overbought and oversold conditions.
  
• Top-Right Data Table:
  A live table displays Upper, Middle, and Lower Prediction values, updating in real time for quick reference without scanning the chart.
  

⯁ USAGE

• Use the regression midline to gauge underlying market bias; green slopes suggest continuation, magenta slopes caution for weakness.
  
• Watch dashed extrapolated ranges as potential targets or reaction zones during upcoming sessions.
  
• Price labels and table values act as precise reference levels for planning entries, exits, or stop placement.
  
• Increase Degree for more curve-fitting on choppy markets, or keep it low for broader trend approximation.
  
• Adjust Period and Extrapolate length to balance stability vs. responsiveness.
  

⯁ CONCLUSION
The Polynomial Regression Channel offers a mathematically advanced way to visualize price trends and anticipate future paths. With matrix-driven polynomial fitting, extrapolated projections, and integrated live labels, it combines statistical rigor with practical trading visuals — a robust upgrade over standard regression channels.