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Technical Studies Reference

Linear Regressive Slope

This study calculates and displays a moving Linear Regressive Slope. The independent variable is the Index \(t\), and the dependent variable is specified by the Input Data Input.

Let \(X\) be a random variable denoting the Input Data, and let \(X_t\) be the value of the Input Data at Index \(t\). Let the Input Length be denoted as \(n\). Then we denote the Linear Regressive Slope at Index \(t\) for the given Inputs as \(LRS_t(X,n)\), and we compute it for \(t \geq n\) as follows.

\(\displaystyle{LRS_t(X,n) = \frac{n\cdot\sum_{i = t - n + 1}^t (t - i)X_i - \sum_{t - n + 1}^t X_i}{\frac{n^2(n - 1)^2}{4}-n\cdot\frac{(n - 1)n(2n - 1)}{6}}}\)

For an explanation of the Sigma (\(\Sigma\)) notation for summation, refer to our description here.



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*Last modified Friday, 08th June, 2018.