Interactive Least Squares Visualization

Interactive Least Squares Learning Tool

Adjust the red line using the sliders below to try to minimize the sum of squared errors. The blue squares show the squared residuals!

Intercept \(\hat\beta_0\)

1.5

Slope \(\hat\beta_1\)

1

Show Optimal

Your Line
y = 1.50 + 1.00x

Optimal Least Squares
y = 1.50 + 1.00x

Your SSE
0.00

Optimal SSE
0.00

Key Concepts

Goal: Find the line \(\hat{y} = \hat\beta_0 + \hat\beta_1x\) that minimizes the Sum of Squared Errors (SSE)

The blue squares show the squared residuals - their total area equals the SSE!

What to Try:

  • Adjust the sliders to minimize the total area of blue squares
  • Try to match the optimal (green) line
  • Notice how the squares get smaller as you approach the optimal solution