Direct Answer
The linear regression angle is the angle, in degrees, of the fitted regression line, computed as the arctangent of its slope. It expresses the steepness of the trend as an angle between -90 and +90 degrees. Positive angles are rising trends and negative angles falling ones, and an angle near 0 is a flat trend.
Linear Regression Angle: Formula, Meaning, Signals, Examples and How to Use It
How Is Linear Regression Angle Calculated?
The linear regression angle is the angle, in degrees, of the fitted regression line, computed as the arctangent of its slope. It expresses the steepness of the trend as an angle between -90 and +90 degrees.
Formula: angle = atan(slope) * 180 / pi
Inputs:
- Regression slope
- Chart or normalization scale for price and time
Worked example. A slope of 0.5 units per bar corresponds to an angle of 26.57 degrees. The inputs are illustrative numbers, not market data.
Reading it. Positive angles are rising trends and negative angles falling ones, and an angle near 0 is a flat trend. Larger absolute values mean steeper fitted movement.
Limits. The angle depends on the units of price and time, so the same data gives different angles on different scales unless slope is normalized first. Comparisons across instruments are only valid with that normalization.
What is Linear Regression Angle?
The linear regression angle is the angle, in degrees, of the fitted regression line, computed as the arctangent of its slope. It expresses the steepness of the trend as an angle between -90 and +90 degrees.
How to use Linear Regression Angle
Positive angles are rising trends and negative angles falling ones, and an angle near 0 is a flat trend. Larger absolute values mean steeper fitted movement. A reading alone is never a buy or sell signal; it needs context from price structure, volume, volatility and the broader market regime.
Strengths
- Converting slope to an angle bounds the number between -90 and +90 degrees, so very steep slopes do not produce unbounded values.
- The angle's sign shows rising or falling and its size shows steepness, which is easy to read on a chart.
- Reproducible when the formula and data convention are fixed.
Weaknesses and limitations
- Arctangent flattens at steep slopes, so differences between very steep trends are compressed into small angle changes.
- The result is a monotone transformation of the slope and adds no information beyond it, so series are ordered the same as by slope.
- Correlated indicators can create false confidence by repeating the same underlying information.
Editorial and risk note
This page is educational content, not individualized investment advice. It should not imply guaranteed prediction, accuracy or outperformance.
Frequently Asked Questions
Is Linear Regression Angle a buy or sell signal?
No. Positive angles are rising trends and negative angles falling ones, and an angle near 0 is a flat trend. The angle depends on the units of price and time, so the same data gives different angles on different scales unless slope is normalized first. A trade built on it still needs a trigger, an invalidation rule, a position size and realistic execution assumptions.
What is the best setting for Linear Regression Angle?
Linear Regression Angle is computed from regression slope; chart or normalization scale for price and time, so the choices that matter are the data convention and the window it is read over. Test those across instruments, regimes and out-of-sample periods instead of fitting one historical winner.
Can Linear Regression Angle be used by itself?
The angle depends on the units of price and time, so the same data gives different angles on different scales unless slope is normalized first. Comparisons across instruments are only valid with that normalization. For that reason it is read next to measures of direction, participation, valuation, liquidity and risk, not alone.
Does Linear Regression Angle work on every timeframe?
The calculation (angle = atan(slope) * 180 / pi) can be run on any bar size, but behavior is not portable: a reading on a five-minute chart describes a very different market window from the same reading on a daily chart. Validate the exact timeframe before relying on it.
Why does Linear Regression Angle give false signals?
Arctangent flattens at steep slopes, so differences between very steep trends are compressed into small angle changes. The result is a monotone transformation of the slope and adds no information beyond it, so series are ordered the same as by slope. Lag, noise and regime changes add to this, because market participants react to new information after the reading is calculated.
How should Linear Regression Angle be backtested?
Rebuild Linear Regression Angle from regression slope using point-in-time data, write the rules before testing, include delisted securities where relevant, model realistic fills and costs, reserve a validation sample and compare with a simpler baseline.