Linear regression is a statistical tool used to predict future values from past values. In the case of security prices, it is commonly used to determine when prices are overextended.
A Linear Regression trendline uses the least squares method to plot a straight line through prices so as to minimize the distances between the prices and the resulting trendline.
If you had to guess what a particular security's price would be tomorrow, a logical guess would be "fairly close to today's price." If prices are trending up, a better guess might be "fairly close to today's price with an upward bias." Linear regression analysis is the statistical confirmation of these logical assumptions.
A Linear Regression trendline is simply a trendline drawn between two points using the least squares fit method. The trendline is displayed in the exact middle of the prices. If you think of this trendline as the "equilibrium" price, any move above or below the trendline indicates overzealous buyers or sellers.
A popular method of using the Linear Regression trendline is to construct Linear Regression Channel lines. Developed by Gilbert Raff, the channel is constructed by plotting two parallel, equidistant lines above and below a Linear Regression trendline. The distance between the channel lines to the regression line is the greatest distance that any one closing price is from the regression line. Regression Channels contain price movement, with the bottom channel line providing support and the top channel line providing resistance. Prices may extend outside of the channel for a short period of time. However if prices remain outside the channel for a longer period of time, a reversal in trend may be imminent.
A Linear Regression trendline shows where equilibrium exists. Linear Regression Channels show the range prices can be expected to deviate from a Linear Regression trendline.
The following chart shows the Japanese Yen with a Linear Regression Channel.
The linear regression formula is:
Information for this article was derived from the book, Technical Analysis from A to Z by Steven B. Achelis