r-squared

Description

The Linear Regression method provides several useful outputs for technical analysts, including the r-squared. R-squared shows the strength of trend. The more closely prices move in a linear relationship with the passing of time, the stronger the trend. 

Interpretation

r-squared values show the percentage of movement that can be explained by linear regression. For example, if the r-squared value over 20 days is at 70%, this means that 70% of the movement of the security is explained by linear regression. The other 30% is unexplained random noise.

It is helpful to consider r-squared in relation to Slope. While Slope gives you the general direction of the trend (positive or negative), r-squared gives you the strength of the trend. A high r-squared value can be associated with a high positive or negative Slope.

Although it is useful to know the r-squared value, ideally, you should use r-squared in tandem with Slope. High r-squared values accompanied by a small Slope may not interest short term traders. However, high r-squared values accompanied by a large Slope value may be of huge interest to traders.

One of the most useful way to use r-squared is as a confirming indicator. Momentum based indicators (e.g., Stochastics, RSI, CCI, etc.) and moving average systems require a confirmation of trend in order to be consistently effective. R-squared provides a means of quantifying the “trendiness” of prices. If r-squared is above its critical value and heading up, you can be 95% confident that a strong trend is present. 

When using momentum based indicators, only trade overbought/oversold levels if you have determined that prices are trendless or weakening (i.e., a low or lowering r-squared value). Because in a strong trending market, prices can remain overbought or oversold for extended periods. Therefore, you may want to reconsider trading on strict overbought/oversold levels used by many indicators. An “overbought” market can remain overbought for extended periods in a trending market.  However, a signal generated by a moving average crossover system may be worth following, since these systems work best in strong trending markets.

To determine if the trend is statistically significant for a given x-period linear regression line, plot the r-squared indicator and refer to the following table. This table shows the values of r-squared required for a 95% confidence level at various time periods. If the r-squared value is less than the critical values shown, you should assume that prices show no statistically significant trend.

You may even consider opening a short-term position opposite the prevailing trend when you observe r-squared rounding off at extreme levels. For example, if the slope is positive and r-squared is above 0.80 and begins to turn down, you may consider selling or opening a short position.

There are numerous ways to use the linear regression outputs of r-squared and Slope in trading systems. For more detailed coverage, refer to the book The New Technical Trader by Tushar Chande and Stanley Kroll.