R-Squared

A linear regression method that helps quantify the strength of market trends (i.e. “trendiness of prices).

Overview

The more closely prices move in a straight line over n-periods (forming a linear relationship), the stronger the trend. R-Squared values represent the percentage of price movement that can be explained by linear regression. For example, if the R-Squared value over 14 periods is at 50% then that means that 50% of the price movement can be explained by linear regression and the remaining 50% is random noise.

R-Squared method as a technical indicator plotted on AUD/NZD Daily Chart 4/3/2011

Source: VT Trader

Interpretation

To determine if a trend is statistically significant for an n-periods linear regression line a 95% confidence level is required. The 95% confidence level varies based on the number of periods being evaluated. If the R-Squared value is less than its corresponding 95% confidence level for a given n-periods it is generally assumed that no statistically significant trend exists. The table below outlines the recommended number of R-Squared periods and their corresponding 95% confidence levels.

# of Periods / R2 Critical Value (95% Confidence)
5  / 77
10 / 40
14 / 27
20 / 20
25 / 16
30 / 13
50 / 8
60 / 6
120 / 3

There are many ways to use linear regression and R-Squared to generate potential trading opportunities.

One such method recommends using R-Squared in conjunction with the Linear Regression Slope. R-Squared defines the strength of the trend and the Linear Regression Slope defines the general direction of the trend (positive or negative). Potential trading signals would be generated with respect to the direction of the Linear Regression Slope while the R-Squared remained above its 95% confidence level.

Another method recommends using R-Squared in conjunction with oscillators. Potential trading signals would be generated with respect to the oscillator’s overbought and oversold levels while R-Squared remains low (i.e. well below its 95% confidence level) indicating that prices are less “trendy”.

For additional information you may wish to refer to Tushar Chande’s and Stanley Kroll’s book entitled, “The New Technical Trader”.