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2004issue C031

Building a daily score from regression, retracement, and volume

A daily-chart construction fits a linear-regression midline over a zigzag-defined lookback, then adds Fibonacci retracement bands and a volume-slope check. Editorial: stack those terms so each method can be audited or removed without treating the whole setup as one visual pattern.

  • The lookback window is one plus the bars since the latest 20 percent close-based zigzag pivot, and a score is issued only when that window is between 10 and 60 trading days.
  • Linear regression fits a least-squares midline to closes; residual slopes of accumulated closes below and above that midline must point back toward the line.
  • Fibonacci retracement is pullback depth as a percent of the prior swing range, gated at the 20, 38, and 50 percent bands used in this construction.
  • When the gates pass, the composite formation score adds points for lookback length, a low coefficient of determination, shallow retracement, and a negative volume slope, and it is retained only when that integer is greater than zero.
Entries in this reading3 entries

A daily chart built from stacked terms

The construction is specified for daily charts. It keeps formations lasting at most 60 trading days with retracements of no more than 50 percent.

Editorial: read the setup as stacked, inspectable terms, a linear-regression midline first, then Fibonacci-style retracement bands and a volume-slope check, so each method can be audited or removed without treating the whole setup as one visual pattern.

Zigzag swings and the lookback window

Swing location uses a 20 percent close-based zigzag, and the construction is specified to need at least four such swings already present in the chart history.

Lookback length I is one plus the bars since the latest zigzag pivot. The lookback-window is that bar count from the latest zigzag pivot, and a score is issued only when the count falls between 10 and 60 trading days.

Linear regression as the first term

Linear regression is a least-squares midline, slope, and coefficient of determination fitted to ordered closes over a defined lookback, with the same slope form reused on residuals and on volume. A linear-regression slope of closes over I defines the local regression midline.

Residual slopes and a short-term swing count

Closes below and above that midline are accumulated only after the prior pivot date, and separate least-squares slopes are then taken of those down and up residual series. Residual-slopes are those separate least-squares slopes of accumulated closes below and above the regression midline, required to point back toward that line.

A short-term swing count tallies, over the open lookback, crossings between a 5-period simple moving average of the close and the regression midline.

Retracement bands and volume participation

Fibonacci retracement is pullback depth measured as a percent of the prior swing range and gated at the 20, 38, and 50 percent bands used in this construction. Maximum retracement is the greater of the current close's distance to the lookback high or lookback low, divided by the prior zigzag-leg price span and expressed as a percent.

Volume-price analysis is reading participation from the sign of volume's lookback slope together with how price residuals sit around the regression midline. Volume participation is measured as the least-squares slope of volume over the same lookback I.

Gates and the composite formation score

The composite score is evaluated only when I is between 10 and 60 inclusive, the down-residual slope is positive, the up-residual slope is negative, retracement is under 50, and the short-term swing count is at least 3.

When those gates pass, discrete points are added for lookback length (2 if I is at least 15 and under 30; 1 if I is 30 through 55), for a low coefficient of determination of closes (2 if under 0.2; 1 if at least 0.2 and under 0.5), for shallow retracement (4 if under 20; 3 if at least 20 and under 38), and for a negative volume slope (4 points). The composite-formation-score is an integer assembled from time, coefficient of determination, retracement depth, and volume-slope points and retained only when it is greater than zero.

Educational research material, not investment advice. Historical source context does not establish present-day performance.
33 of 43 in the Linear regression track
20041-1 pp.Next on Linear regressionConstructing least-squares trendlines from ordered pricesA least-squares fit is the unique straight line that minimizes the sum of squared vertical misses from an ordered sample, and it is fully specified by an intercept and a slope.
All readings on this track · 43 readings
  1. 1990Constructing dollar baselines from rates, inflation, and residuals
  2. 1990Constructing a nominal index value from forward earnings and fitted yield
  3. 1990Constructing a nominal index price from earnings and a fitted yield
  4. 1990Endpoint-pinned price paths are not forecasts
  5. 1990Constructing least-squares polynomial smoothers
  6. 1991Endpoint growth rates versus linear-regression consistency
  7. 1991Out-of-sample checks for linear growth fits
  8. 1991Trend as persistence, not a straight line
  9. 1991Quadratic trend, residual oscillator, and a secondary cycle calendar
  10. 1991Time-origin offset and residual-price divergence on a quadratic least-squares fit
  11. 1991A least-squares trendline from ordered prices
  12. 1992Constructing log-linear growth and reliability screens
  13. 1992Constructing log-linear growth-rate baselines
  14. 1992Next-session high, low, and close from rolling linear regression
  15. 1993Auditing an index price-earnings multiple with short-rate regression
  16. 1994Regression-seeded nested exponential price filter
  17. 1994Constructing the double exponential average from lag cancellation
  18. 1994Evaluating money supply as a linear leading-index baseline
  19. 1995Constructing least-squares trend channels
  20. 1995Linear baseline holdout checks for annual bill-rate forecasts
  21. 1995Projection bands from high and low regression slopes
  22. 1995Evaluating a least-squares end-point moving average on a known test series
  23. 1996Constructing an endpoint moving average from a least-squares line
  24. 1996Scoring equity path consistency with a k-ratio overlay
  25. 1996Evaluating month-end yield gaps for equity regimes
  26. 1996Constructing session-indexed standard error bands
  27. 1998Evaluating linear regression baselines for index valuation
  28. 1998R-squared as a two-state trend filter from a price-time fit
  29. 2000Second-order moving-average lag correction
  30. 2002Price regression line versus beta for index tracking
  31. 2003Regression slope with an r-squared trend confidence gate
  32. 2003Constructing finite-volume-element divergence with slope comparison
  33. 2004Building a daily score from regression, retracement, and volume
  34. 2004Constructing least-squares trendlines from ordered prices
  35. 2007Rectangle breakout targets beyond height
  36. 2007Confirming a price trend with regression slope and r-squared
  37. 2008A linear-regression angle assembled as one trend filter
  38. 2010A two-state swing machine from four running extremes
  39. 2016Score oil-complex tightness before divergence or regression
  40. 2017Nikkei-yen intermarket divergence as a regime case study
  41. 2017Constructing Calmar ratio and linear regression baselines
  42. 2019Pair-trade layer construction versus average-spread management
  43. 2020A convolution slope built from nested linear regression
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