Studies: Linear Regression and r-Squared

The following example was created by applying three Linear Regression Channel studies to the chart, and configuring them as shown below in the images of the property forms.  This illustrates the flexibility of this one study. 

R-Squared is a measure of association beetween the linear regression and the underlying data.  It identifies how closely the regression line matches the price movement.  The higher the r-squared value, the greater the correlation with the trending price.  Though r-squared is a value between zero and 1.0, it is rescaled in Ensign to plot on a percent scale from 0..100 to be similar to the Stochastic and the Relative Strength Index scaling.

A rising r-squared indicates the price is trending.  A declining r-squared indicates the trend is weakening, or non-trending.  Note the rising r-squared at points 1, 2 and 3, when the market began to trend, and the subsequent decay in r-squared when the top or bottom was formed by the market moving sideways.

Linear Regression Slope (LRS) is the 1st derivative of the Linear Regression Indicator.  It can be used show the direction of the Linear Regression Indicator.  LRS remains above the zero line during strong price climbs, and below zero during strong price declines.  During sideways movements, the LRS remains near the zero line.