The Geometry of Least Squares

The Geometry of Least Squares Drag points to see how r and the squares react. The Geometry of Least Squares lets you explore this hands-on instead of only reading about it.

Investigate the relationships between two quantitative variables through scatterplots, correlation, and linear regression models. It focuses on Scatterplots (Direction, Form, Strength), Correlation Coefficient (r), Least-Squares Regression Line (LSRL), Residuals and Residual Plots, Coefficient of Determination (r-squared), Influential Points and Outliers from the “Unit 2: Exploring Two-Variable Data” section.

You can drag elements directly on the canvas; toggles show or hide layers so you can compare cases; the “Add Outlier”, “Reset Linear”, “Clear All” buttons run actions or reset the demo. Every change updates the visualization in real time, so you can see exactly how each variable affects the outcome.

AP Statistics introduces students to the major concepts and tools for collecting, analyzing, and drawing conclusions from data. The course is equivalent to a one-semester introductory college statistics course and focus… This demo is the interactive piece for the “Unit 2: Exploring Two-Variable Data” section. Open the full AP Statistics course wiki at https://www.getlykke.com/explore/public/ap-statistics-70553ac9-70f9-422d-b8b6-c328240d85c1 for notes, flashcards, quizzes and the other demos.

You'll build intuition for Scatterplots (Direction, Form, Strength), Correlation Coefficient (r), Least-Squares Regression Line (LSRL), Residuals and Residual Plots, Coefficient of Determination (r-squared), Influential Points and Outliers — and, crucially, see how they behave when you change the inputs, which is hard to get from a textbook or lecture on AP Statistics alone.