Regression and an influential point: move an observation

The relationship to understand

b₁=cov(x,y)/sₓ², b₀=ȳ−b₁x̄; r=cov(x,y)/(sₓsᵧ).

Try it and interpret

Move the orange point, then turn it off. Compare the two lines and r, paying attention to its position in the scatter rather than only to the p-value.

Assumptions and limitations

Teaching points, not research data. A point far away in x has leverage, but its influence also depends on its departure from the fitted relationship. Always inspect the scatter and residuals.

Go further with the course

This page focuses on one concept. The full chapter (French) contains the reasoning, further examples, slides and FAQ. Demonstration values are computed or constructed within the stated model; they are not new research findings.