Linear Regressions 1

This discussion is meant to go over a functional elementary approach to using linear regressions and standard deviations off of linear regressions of variable time frames. Text book definitions will be avoided, and references to the math used will be kept to a minimum, google searches give enough resources on this.

One way to look at a linear regressions is to view it as a trend line. It is not a trend line connecting lows or other particular price data. It is best approached as a trend line that includes all price data. It does not connect various price points, but instead bisects all price points for a specified period in time. Below are three charts of Agilent Technologies Inc. The green line bisecting the bars on the chart is a 10 day linear regression. As the prices change, the slope(angle) of the linear regression line changes to fit the most current 10 days of data.

A - Agilent Technologies Inc. (click to enlarge)


A - Agilent Technologies Inc. (click to enlarge)


A - Agilent Technologies Inc. (click to enlarge)

These three charts show how the slope of these regressions changes and follows the most current 10 days of price data. While a 10 day linear regression might not be of much use, comparing the slope of the 10 day to a longer term, 50 day, might be incorporated into a larger data scan. Below is a chart of Agilent Technologies Inc. with a 50 day linear regression(Blue Line) and the 10 day linear regression(Green Line).

A - Agilent Technologies Inc. (click to enlarge)


This 50 day linear regression shows that prices over this time frame are moving lower in steady fashion. Looking at a linear regression line alone doesn't provide much help other than showing the general trend or slope of prices. One tool to apply to a linear regression is standard deviation lines. In the same chart above, the 50 day linear regression line will have two lines applied. One will be 2 standard deviations above and one 2 standard deviations below this linear regression. With 2 standard deviations above and below, 95% of prices should take place inside these limits.

A - Agilent Technologies Inc. (click to enlarge)


This chart shows how most prices are contained inside these two lines. Fighting the slope of the linear regression and entering trades at the upper standard deviation line can make life difficult. This is an introduction to provide a basis for the next series of articles to follow on how to incorporate these tools into any trading system or investment strategy. If there are ever any questions, feel free to send questions and comments using the button on the right side of the page above the blog archive.