Linear Regression Lines

In statistics, the "linear regression line" is a method that allows predicting future values from a distribution of past values.
In the case of stock technical analysis, this method is commonly used to determine when prices exit the ongoing trend.

The Linear Regression Line is a line drawn between two points using the "least squares" method. This line is calculated in such a way that the sum of the squared deviations (i.e. the sum of the squares of the deviations between the price on a given day and the point on the line directly above or below that price) is minimized.
This line therefore represents the "best average approximation" of the price position over the considered period.

To obtain the linear regression line over a given period, you can use the closing prices or the highest, lowest, or median prices.

Conventionally in Technical Analysis as introduced by Gilbert Raff, the linear regression line is used to define a channel with two parallel lines equidistant above and below the linear regression line.
The distance between one of the channel lines and the linear regression line is called the "standard deviation" corresponding to the average of the squared deviations of prices relative to the linear regression line over the fixed period.

Example

Interpretation

The linear regression line shows a "balanced" price evolution. The channel determined from this line indicates where one can expect a price evolution similar to the trend and volatility that were prevailing during the selected period.
For this reason, the two parallel lines forming the channel can be considered as support and resistance lines.

Prices may exit this channel for a short period. But if this exit lasts, it is a sign of an imminent trend reversal.

Notes

1. In Axial Finance, two channels are actually drawn, the narrower one corresponding to a distance from the linear regression line of one standard deviation, the wider one at a distance of two standard deviations.
2. In Axial Finance, for intraday price charts, the plotting period of the Linear Regression Line and the channel is systematically equal to the number of days chosen for the intraday price display.