Confirming trend with regression slope and r-squared

Two filters from one fitted line

A linear-regression line is a least-squares best-fit through recent prices. It reduces bar-to-bar noise and is the shared baseline for the two readings used here: r-squared and linear-regression slope.

R-squared is a zero-to-one association measure that shows how closely that line tracks the price series it is fitted to. Linear-regression slope measures the per-bar change of the same fitted line, not the raw price series.

Editorial interpretation: treat r-squared as a trend-strength filter and linear-regression slope as a direction filter. A price move is treated as a confirmed trend only when both agree with a moving-average crossover and the stochastic oscillator. Without that agreement, the same move is treated as a possible countertrend rally.

How r-squared measures trend association

Rising r-squared marks stronger trend association. Falling values mark weakening association. The reading does not identify price direction. A rising value can accompany either advancing or declining prices.

The r-squared threshold for a 95% positive correlation depends on lookback length. A 10-period reading needs about 0.40, a 20-period reading needs 0.20, and a 50-period reading needs about 0.08.

A 20- to 30-period r-squared lookback is presented as practical for end-of-day work. The examples use a 20-period setting that matches the regression length.

R-squared reversals from levels above 0.70 are treated as warnings of a possible near-term price change. Declines from high levels often coincide with flattening or rounding of the regression line.

How slope reads direction

Linear-regression slope is the per-bar change of the fitted line. It is plotted around zero so that a positive reading points up and a negative reading points down.

A reading above zero is read as upward direction. A reading below zero is read as downward direction. Slope answers the direction question that r-squared leaves open.

Agreement with crossovers and the stochastic oscillator

A moving-average crossover is a dual moving-average signal used as a price-structure confirmation, not as a standalone entry rule. The stochastic oscillator is a momentum oscillator used to flag overbought or oversold conditions and possible countertrend rallies that still need regression confirmation.

When a moving-average crossover and a rising stochastic oscillator are not joined by r-squared above the 0.20 threshold and a positive slope, the combination is treated as a possible countertrend rally rather than a confirmed uptrend.

Late confirmation and failed confirmation

In the gold example, later confirmation by both regression outputs arrived after the stochastic oscillator was already overbought and the moving averages had widened, after which price rose an additional 45 points.

A rising stochastic oscillator and rising r-squared can still fail as trend confirmation if linear-regression slope stays negative and price cannot clear a short-term moving average. Strength of association is not enough when the fitted line is still pointing down.

What the paired filters can and cannot do

The paired regression filters are described as useful for judging trend strength, skipping some short-lived false moves, and flagging fading momentum.

They still miss exact tops and bottoms. They also produce conflicts in sideways or transitional markets, where r-squared, slope, the moving-average crossover, and the stochastic oscillator need not point the same way.

Editorial interpretation

This is a TradersWeek editorial reading of the archive workflow, not a claim from the archive. R-squared is the trend-strength filter. Linear-regression slope is the direction filter. The moving-average crossover supplies price-structure confirmation. The stochastic oscillator flags momentum extremes and possible countertrend rallies.

Editorial interpretation: agreement across those readings is the bar for calling a confirmed trend. Disagreement, especially a negative slope or r-squared below the lookback threshold, keeps the move in the countertrend-rally category.