In trading linear regression is the analysis of 2 variables price and time  basically an algorithm. The 2 lines are graphically displayed by an indicator (or can be drawn)  the parallel lines comprise a price channel where price action is prominent. In general more bars will yield a larger channel. The upper trend line of the channel serves as the resistance and the lower trend line serves as support. If there is a center line it serves as an equilibrium point which usually has a slope. All lines will actually slope together at a fixed distance from each other unless the channel resets. The slope depicts the trend direction.
The name "linear" refers to a straight line while "regression" (a statistical term) is the relationship between the mean value of a random variable and the corresponding values of one or more independent variables. In trading we are most concerned with the variables of time and price.
Example of linear regression in statistics:
Background  Historically
Linear regression was the first type of regression analysis to be studied rigorously in statistics (used first in astrology) and it was later incorporated into financial theories. The first form of regression was "The method of least squares" circa 1794 by Carl Friedrich Gauss when he was only 17 or 18 but the method was not published until 1809. Gauss's method was applied to track a newly discovered asteroid called "Ceres". The method is not considered perfect but was a breakthrough in science, mathematics, and statistics. Gauss is ranked as one of history's most influential mathematicians.
It took awhile for regression analysis to be used in trading and even longer to become popular. In the 50's  60's economist used desk calculators to calculate regressions. Before the 70's it could take up to 24hrs to receive the result from one regression. Today regression analysis is very common in trading and new methods have been developed. Where it once took nearly 24hrs  today a channel can be drawn in a fraction of a second by advanced indicators like the one's I use in mt4.
The principle
Prices usually exceed the channel frames for a short time. If they keep outside of the channel frames for a longer time than usual, it forecasts the possibility of trend turn. The big idea is to define a previous trend, hopefully predict it's trajectory, and establish support and resistance points. If price action stays within an established channel it can be good points of entry or exit at or near the tops and bottoms  additionally if price breaks the channel it can be a possible reversal. In essence it is a probability theory. As with all trading strategies: experiement, set a stop loss, and set a target price. Never float a trade without a plan.
By Neal Vanderstelt
Forex Trader, Market Analyst, Trading System Designer
forexmetatrader charting, indicators, information portal about currencies
Sunday, December 25, 2011
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