Linear regression and standard deviation channels

الفكرة بكلمات بسيطة

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).

طريقة الحساب

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

كيفية الاستخدام

• 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.

استخلاص النتائج

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

ما يجب الانتباه إليه

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

لمحة تاريخية

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