# 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.