/**
* Linear Regression Indicator
* Calculates linear regression line and related statistical measures for trend analysis
*/
/**
* Calculate Linear Regression for price data
* @param prices Array of prices (typically closes)
* @param period Period for regression calculation (default 20)
* @returns LinearRegressionData object
*/
export function calculateLinearRegression(prices, period = 20) {
if (prices.length < period) {
return null;
}
// Use the most recent 'period' prices
const data = prices.slice(-period);
// Calculate linear regression using least squares method
const n = data.length;
const sumX = (n * (n - 1)) / 2; // Sum of x values (0 to n-1)
const sumY = data.reduce((sum, price) => sum + price, 0);
const sumXY = data.reduce((sum, price, index) => sum + (price * index), 0);
const sumXX = data.reduce((sum, _, index) => sum + (index * index), 0);
// Calculate slope and intercept
const slope = (n * sumXY - sumX * sumY) / (n * sumXX - sumX * sumX);
const intercept = (sumY - slope * sumX) / n;
// Current regression line value (at the last point)
const regressionLine = intercept + slope * (n - 1);
// Calculate R-squared
const yMean = sumY / n;
const ssTot = data.reduce((sum, price) => sum + Math.pow(price - yMean, 2), 0);
const ssRes = data.reduce((sum, price, index) => {
const predicted = intercept + slope * index;
return sum + Math.pow(price - predicted, 2);
}, 0);
const rSquared = 1 - (ssRes / ssTot);
// Calculate standard error
const standardError = Math.sqrt(ssRes / (n - 2));
// Calculate correlation coefficient
const correlation = Math.sqrt(Math.max(0, rSquared)) * (slope >= 0 ? 1 : -1);
// Calculate regression bands (2 standard deviations)
const upperBand = regressionLine + (2 * standardError);
const lowerBand = regressionLine - (2 * standardError);
// Determine trend
let trend = 'neutral';
if (slope > 0.001) {
trend = 'bullish';
}
else if (slope < -0.001) {
trend = 'bearish';
}
// Calculate trend strength (based on slope magnitude and R-squared)
const slopeStrength = Math.min(100, Math.abs(slope) * 1000);
const strength = Math.round((slopeStrength + rSquared * 100) / 2);
// Current price vs regression line
const currentPrice = data[data.length - 1];
const priceVsRegression = ((currentPrice - regressionLine) / regressionLine) * 100;
let position = 'on_line';
if (currentPrice > regressionLine * 1.001) {
position = 'above';
}
else if (currentPrice < regressionLine * 0.999) {
position = 'below';
}
return {
slope,
intercept,
regressionLine,
rSquared,
standardError,
correlation,
trend,
strength,
upperBand,
lowerBand,
priceVsRegression,
position
};
}
/**
* Calculate Linear Regression Channel
* @param prices Array of prices
* @param period Period for regression
* @param deviations Number of standard deviations for channel (default 2)
* @returns Channel data with upper and lower bounds
*/
export function calculateLinearRegressionChannel(prices, period = 20, deviations = 2) {
const regression = calculateLinearRegression(prices, period);
if (!regression) {
return null;
}
return {
upper: regression.regressionLine + (deviations * regression.standardError),
middle: regression.regressionLine,
lower: regression.regressionLine - (deviations * regression.standardError)
};
}
