Linear Regression Slope

Name Type Prerequisite Use Cases
Linear Regression Slope (LRS) Momentum OHLC Data Identifying trend strength and potential exhaustion.

Definition

The Linear Regression Slope indicator displays the slope (steepness and direction) of the linear regression line fitted to the price over a specified period. It measures the strength and direction of the trend.

Mathematical Equation

For a rolling window of \(N\) periods, calculate the slope \(m\) of the best-fit line \(y = mx + b\) using the least squares method:

\[ m = \frac{n \sum (xy) - \sum x \sum y}{n \sum x^2 - (\sum x)^2} \]

  • Positive Slope: Uptrend.

  • Negative Slope: Downtrend.

  • High Absolute Value: Strong trend.

Special cases

  • Maximum possible value: Unbounded
  • Minimum possible value: Unbounded
  • Behavior: Oscillates around zero, indicating the angle (momentum) of the linear regression line.

Visualization

Linear Regression Slope

Trading Significance

  1. Trend Strength: The steeper the slope, the stronger the trend.

  2. Trend Reversal: A change in the sign of the slope (crossing zero) indicates a potential change in trend direction.