Figure 1.1: Linear Regression and Residuals

Ordinary Least Squares Estimation

In statistical modeling, the goal of linear regression is to identify the line that minimizes the sum of the squared distances between the observed data and the predicted values. These distances are known as residuals (or errors). Squaring these errors intentionally penalizes large outliers, aggressively pulling the line toward anomalous data points (demonstrated in the Edge Case).

Figure 1.1: A dynamic visualization of a linear model ŷ = β₀ + β₁x. The dashed red lines represent the residuals (e_i). The curly brace on the y-axis explicitly defines the intercept magnitude (β₀).

1. Select Data Distribution:

2. Adjust Model Parameters:

Intercept (β₀): 0.00

Slope (β₁): 0.00

Sum of Squared Errors (SSE): 0.00