Linear Regression Curve

Name Type Prerequisite Use Cases
Linear Regression Curve (LRC) Trend SMA Identifying the "fair value" path of a trend.

Definition

The Linear Regression Curve plots the end values of linear regression lines fitted to a rolling window of prices. It is essentially the same as the Least Squares Moving Average (LSMA). It provides a smoothed representation of the price trend based on statistical regression.

Mathematical Equation

For each point \(t\), fit a line \(y = mx + b\) to the previous \(N\) prices. The curve value is the value of this line at \(t\).

Special cases

  • Maximum possible value: Unbounded
  • Minimum possible value: 0
  • Behavior: Follows the price by mapping the end points of rolling linear regression lines.

Visualization

Linear Regression Curve

Trading Significance

  1. Trend direction: The slope of the curve indicates the trend direction.

  2. Fit: It tends to fit the data better than simple moving averages, reacting faster to price changes.