How Least Squares Fits a Linear Regression Line to Price Data

Summary

This document explains a linear regression line fitted to closing prices over a sequence of time periods. The line has an intercept and a slope: the intercept represents the fitted starting level, while the slope describes how the fitted value changes as the time index advances. The document gives the standard least-squares coefficient formulas in terms of summed time indices, prices, and their products.

Least squares chooses the line that minimizes the distances between observed data points and the fitted line. This makes regression a way to summarize a price series’ linear direction over the selected window. The document does not explain how to turn the line into entry or exit rules, choose a window, or assess predictive value. It provides no empirical results, and a fitted historical trend alone does not establish that future prices will follow it.

Key ideas

• Linear regression models closing price as a linear function of the time index.
• The slope summarizes the fitted price change across the selected periods.
• Least squares selects coefficients by minimizing discrepancies between observations and the line.
• The document gives no trading rules or evidence that the fitted trend predicts future returns.

Tags

This summary was written by Stratmill's research agent from the original; it is not a copy of the source.