Regression slope with an r-squared trend confidence gate

Slope as a signed rate of change

Linear-regression-slope is the signed rate of change from a fitted line over a chosen lookback. It is read as how fast the series is expected to move per sampling interval. A steep slope describes a faster rate of change than a shallow slope.

Slope encodes whether the fitted trend is positive or negative. It does not, by itself, measure how strong that trend is.

R-squared as a strength score

R-squared is the goodness-of-fit of that same line. It is used here as a numeric score of trend strength rather than as a standalone buy or sell flag.

R-squared is read with slope. A high r-squared plus a large positive or negative slope is treated as stronger evidence that a trend is developing.

Keep slope and r-squared on one fitted line

Slope requires a lookback and a price field such as close or a high-low average. R-squared must use that same lookback so both outputs describe one fitted line.

That period-matched-pair keeps the strength score on the identical fitted line.

Critical r-squared at 95%

At a stated 95% confidence level, critical-r-squared falls as the lookback lengthens: 0.77 at 5 periods, 0.40 at 10, 0.27 at 14, 0.20 at 20, 0.16 at 25, 0.13 at 30, 0.08 at 50, 0.06 at 60, and 0.03 at 120.

If r-squared for a given lookback is below the matching critical value, the series is treated as showing no statistically significant trend at that 95% threshold.

Critical-r-squared scales inversely with period length. A 10-period threshold of 0.40 implies 0.08 at 50 periods, with other lengths rounded to two decimal places from the same ratio.

A rising-fit screen

A screen can keep only series whose slope is above zero, whose r-squared exceeds the period’s critical value (0.27 at 14 periods or 0.13 at 30), and whose r-squared is higher than on the prior bar.

The rising-fit-filter requires current r-squared to exceed its prior bar so the fit is strengthening, not rolling over.

Oscillator extremes after the gate

Oscillators that depend on overbought or oversold levels are described as needing this strength check. A high and rising r-squared is treated as 95% confidence that a strong trend is present and those extremes can persist.

Late fits and false crossings

An unusually high r-squared such as 0.8 is flagged as a possible late or stretched condition. Threshold crossings are acknowledged to include false signals.

Editorial reading

TradersWeek editorial interpretation: treat linear-regression-slope as a signed rate-of-change estimate that stays incomplete until the period-matched-pair r-squared clears its critical-r-squared and still passes the rising-fit-filter. Oscillator extremes are then read only after the fitted line itself has been admitted as a significant trend.