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10.32 R-Squared Index

The R-squared indicator by Tushar Chande and Stanley Kroll is a measure of how closely the past N days resemble a straight line, ie. a trend. It calculates what is called in statistics the coefficient of determination of the prices versus a straight line. This coefficient is written r^2, hence the name of the indicator.

For reference, the formulas are as follows, where X values are the closing prices and Y values are a straight line 1,2,…,N. Variance is the square of standard deviation (see Standard Deviation).

         (Covariance X,Y)^2
r^2 = -----------------------
      Variance X * Variance Y

Covariance X,Y = Mean (X*Y) - (Mean X) * (Mean Y)

Variance X = Mean(X^2) - (Mean X)^2

The R-squared indicator ranges from 0 meaning no apparent correlation to the straight line, up to 1 for perfect correlation. The slope of the closing prices line doesn’t matter, nor does the absolute price level, only how well they make a straight line.

Chande and Kroll suggested using a 14-day period, and that’s the default in Chart.

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