Linear regression analyzes two separate variables in order to define a single relationship. In chart analysis, this refers to the variables of price and time. Investors and traders who use charts recognize the ups and downs of price printed horizontally from day-to-day, minute-to-minute or week-to-week, depending on the evaluated time frame. The different market approaches are what make linear regression analysis so attractive. (Learn more about quantitative analysis in

*Quantitative Analysis Of Hedge Funds*.)

**Bell Curve Basics**

Statisticians have used the bell curve method, also known as a normal distribution, to evaluate a particular set of data points. Figure 1 is an example of a bell curve, which denoted by the dark blue line. The bell curve represents the form of the various data point occurrences. The bulk of the points normally take place toward the middle of the bell curve, but over time, the points stray or deviate from the population. Unusual or rare points are sometimes well outside of the "normal" population.

Figure 1: A bell curve, normal distribution. |

Source: ProphetCharts |

*Modern Portfolio Theory Stats Primer*.)

Stock Price as a Data Set

Stock Price as a Data Set

Imagine if we took the bell curve, flipped it on its side and applied it to a stock chart. This would allow us to see when a security is overbought or oversold and ready to revert to the mean. In Figure 2, the linear regression study is added to the chart, giving investors the blue outside channel and the linear regression line through the middle of our price points. This channel shows investors the current price trend and provides a mean value. Using a variable linear regression, we can set a narrow channel at one standard deviation, or 68%, to create green channels. While there isn't a bell curve, we can see that price now reflects the bell curve's divisions, noted in Figure 1.

Figure 2: Illustration of trading the mean reversion using four points |

Source: ProphetCharts |

**Trading the Mean Reversion**

This setup is easily traded by using four points on the chart, as outlined in Figure 2. No.1 is the entry point. This only becomes an entry point when the price has traded out to the outer blue channel and has moved back inside the one standard deviation line. We don't simply rely on having the price as an outlier because it may get another further out. Instead, we want the outlying event to have taken place and the price to revert to the mean. A move back within the first standard deviation confirms the regression. (Check out how the assumptions of theoretical risk models compare to actual market performance, read

*The Uses And Limits Of Volatility*.)

No.2 provides a stop-loss point in case the cause of the outliers continues to negatively affect the price. Setting the stop-loss order easily defines the trade's risk amount.

Figure 3: Filling the mean price |

Source: ProphetCharts |

*Working Through The Efficient Market Hypothesis*.)

Figure 4: Filling the mean price. |

Source: ProphetCharts |

**Truly Universal**

Technicians and quant traders often work one system for a particular security or stock and find that the same parameters won't work on other securities or stocks. The beauty of linear regression is that the security's price and time period determine the system parameters. Use these tools and the rules defined within this article on various securities and time frames and you will be surprised at its universal nature. (For further reading, see

*Bettering Your Portfolio With Alpha And Beta*and

*Style Matters In Financial Modeling*.)