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2007issue C121-9

Confirming a price trend with regression slope and r-squared

Fit a least-squares line to a fixed lookback of closes, then confirm it with signed slope and an r-squared gate. Keep a same-length moving average as the control, not as a rival forecast.

  • A least-squares line on a fixed lookback of closes reduces bar-to-bar noise and serves as a price-trend baseline.
  • Confirmation is assembled from the regression value, the signed slope, and r-squared against the same series.
  • A higher r-squared means the line tracks the trending component more closely; lookback sets the confirmation gate.
  • A same-length moving average is the control comparison, not a second forecast engine.
Entries in this reading2 entries
Current trackLinear regression112 readingsMoving average449 readings

A quieter price-trend baseline

A least-squares line fitted to a fixed lookback of closes is constructed to reduce bar-to-bar noise and serve as a price-trend baseline.

That line is a least-squares best-fit through a fixed lookback of ordered closes. It is used as a lower-lag trend baseline than a moving average of the same length.

Three readings for confirmation

Trend confirmation is assembled from three platform functions: the regression value, the signed slope of that line, and r-squared against the underlying series.

R-squared is the share of price variation explained by the regression line over the same lookback. A higher reading means the line tracks the trending component more closely. A user threshold decides when the fit is strong enough to treat the slope as confirmation.

Reading slope apart from the overlay

Slope is plotted as its own series and recolored when it crosses zero so direction is read independently of the price overlay. Above zero marks upward direction and below zero marks downward direction.

An r-squared gate set by lookback

Lookback is the user-chosen bar count that sets both the regression window and the numeric level at which r-squared is treated as meaningful. The lookback length sets the level at which r-squared is treated as a confirmation gate. A default construction uses length 20 with a 0.2 threshold.

A conventional chart as a check

A two-line moving average and a stochastic oscillator are shown on the same daily chart so the regression stack can be checked against a conventional trend-and-momentum layout.

Coding the line without a library

A closed-form 10-bar construction recovers slope from weighted closes and the same-length moving average. The regression line can then be coded as an overlay plus a lower-pane slope without a built-in library.

Editorial assembly

Editorial. Fit the line first, read the signed slope for direction, then apply the r-squared gate before treating that slope as confirmation. Leave the same-length moving average in place as the control so the overlay is judged against a familiar baseline, not treated as a rival forecast.

Educational research material, not investment advice. Historical source context does not establish present-day performance.
36 of 43 in the Linear regression track
20081-16 pp.Next on Linear regressionA linear-regression angle assembled as one trend filterPrice is first smoothed with a moving average, then a linear regression is fit to that cleaned series over a stated regression length.
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
By fieldTime series and forecasting51 readingsBy year200773 readings
All 112 readings tagged Linear regression
Also on Linear regression5 readings
1990Constructing least-squares polynomial smoothers1990Two clocks for copper: a factor regime, a regression baseline, and leftover moving-average timing1991Trend as persistence, not a straight line1993Constructing walk-forward forecasts with linear and moving-average baselines1994Constructing the double exponential average from lag cancellation