📈
Least Squares Regression Predictor
AP Statistics · Bivariate Data
🎲 Randomize Data
Learning Objectives
Visualize Residuals dynamically (Distance from observed $y$ to predicted $\hat{y}$).
Understand why we square the residuals before summing ($SS_{res}$).
Prove that the LSRL uniquely minimizes the Sum of Squared Residuals.
Key Equations
\( \hat{y} = a + bx \)
Residual: \( e = y - \hat{y} \)
Minimize:
\( \sum (y - \hat{y})^2 = \text{Min} \)
Tags
Statistics
Bivariate Data
LSRL
Residuals
Scatterplot & Residual Minimization Matrix
User Line SSE
0.0
Actual Min SSE
0.0
Visual Elements
Draw Squared Residuals (Boxes)
Reveal True LSRL ($\hat{y}$) Line
User Slope ($b$)
1.00
User Y-Intercept ($a$)
0.00
Goal:
Adjust your slope and intercept to make the Red SSE box value as small as possible. Can you match the true minimum?
Quick Quiz
Why do we square the residuals instead of taking the absolute value?
Squaring makes the numbers smaller and easier to add.
To strictly penalize large outliers and make calculus/derivation of the minimum slope mathematically possible.
Because negative numbers cannot exist in statistics.