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 (see Linear Regression 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.

If the R-Squared indicator falls below the critical values shown below, it would illustrate no correlation between the price and the Linear Regression Trendline.

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 details, please refer to the book The New Technical Trader by Tushar Chande and Stanley Kroll.

  

Calculation:

             r_s = Realized return

             r_rf = Risk-free rate of return

             StdDev = Standard Deviation indicator

 

Inputs:

Security = XU030

Reference Security = XU100

   Indicates risk-free asset.

Start Day = First day of the date range

End Day = Last day of the date range

Currency

Indicator Type: Trend