Linear regression and standard deviation channels

L’idée en termes simples

Instead of picking points by eye, let maths draw the line that best fits the prices. The outer lines show the normal spread (standard deviation channel) or the widest deviation (regression channel).

Mode de calcul

Click the start and the end of the period. The centre line is the least-squares line through the closes. Standard deviation channel: ± 2 standard deviations; regression channel: ± the largest distance.

Centre = a + b × t (least-squares fit of the closes)
Std-dev channel: centre ± 2 × standard deviation of the distances
Regression channel: centre ± maximum distance

Comment l’utiliser

• Prices near the outer lines are stretched relative to the trend; near the centre, fairly valued.
• The slope of the centre line is the average trend over the period.

Tirer des conclusions

• A close outside a standard deviation channel is statistically unusual.

Points de vigilance

• The channel changes when you change the period: choose it deliberately.

Un peu d’histoire

Least squares was published by Legendre (1805) and Gauss; Francis Galton coined "regression" in the 1880s.