Algorithmic Trading & Indicators Intermediate

Calculate Linear Regression Channel, Slope & R-Squared Trend Strength in Python

Compute least-squares linear regression trendlines, upper/lower standard error channels, and R-squared trend linearity in Python Pandas.

#pandas#numpy#scipy

Problem Statement

Visual trendlines are subjective. Least-squares linear regression channels calculate objective slope, intercept, and R-squared goodness-of-fit to quantify trend linearity.

Formula / Core Logic

y = mx + c computed via scipy.stats.linregress over rolling N periods.

Installation

pip install pandas numpy scipy

linear-regression-channel-slope-momentum-python.py

import pandas as pd
import numpy as np
from scipy.stats import linregress

def linear_regression_channel(df, window=50, num_std=2.0):
    df = df.copy()
    slopes, intercepts, r_sqs, uppers, lowers = [], [], [], [], []
    closes = df['Close'].values
    
    for i in range(len(closes)):
        if i < window:
            slopes.append(np.nan); intercepts.append(np.nan); r_sqs.append(np.nan); uppers.append(np.nan); lowers.append(np.nan)
            continue
        y = closes[i - window + 1 : i + 1]
        x = np.arange(window)
        slope, intercept, r_val, p_val, std_err = linregress(x, y)
        current_val = slope * (window - 1) + intercept
        channel_width = std_err * window * num_std
        slopes.append(slope); intercepts.append(intercept); r_sqs.append(r_val ** 2)
        uppers.append(current_val + channel_width); lowers.append(current_val - channel_width)
        
    df['Reg_Slope'] = slopes
    df['Reg_R2'] = r_sqs
    df['Reg_Upper'] = uppers
    df['Reg_Lower'] = lowers
    return df

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Frequently Asked Questions

Q: What does an R-squared value close to 1.0 signify?

An R-squared value above 0.85 indicates an exceptionally stable, linear trend channel with minimal noise.