Linear Regression Channel: the best-fit line and its error bands

What it measures

A linear regression channel fits a least-squares straight line through the closes of a lookback window, then places bands above and below it at a multiple of the standard error of that fit.

The line is the trend as a statistician would define it: the straight line that minimises squared distance from the data. The bands describe how well price has been sticking to it.

Narrow bands mean the trend has been orderly; wide ones mean the line is a poor summary of what happened.

How it is calculated

These are the steps Basis performs, verified against the published definition.

1. 1

   Fit a least-squares line through the closes of the window, where x is the bar index.

2. 2

   Compute the standard error — the root mean square distance of the closes from that fitted line.

3. 3

   Place the bands at the line plus and minus the multiplier times the standard error.

4. 4

   Recompute the whole fit on every bar, which is why the channel moves as new data arrives.

Settings

A hundred-period window with two standard errors is a common setting. The window defines what trend you are measuring; the multiplier only decides how much of the noise the bands enclose.

How to read it

• The slope is the trend rate, in price per bar, which is a more precise statement than "it is going up".
• Price at the lower band in a rising channel is the conventional pullback entry; price outside the band is either exhaustion or a change of regime, and the channel cannot tell you which.
• A channel whose bands are widening is a trend losing its structure even while the slope stays positive.

Where it misleads

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