Correlation, significance and R²: distinguish the concepts

The relationship to understand

t=r√[(n−2)/(1−r²)]; for simple linear regression with an intercept, R²=r²=1−SSE/SST.

Try it and interpret

With r=0.10, R² always equals 1%. Increasing n from 30 to 1000 changes the theoretical p-value from about 0.599 to 0.0015, without increasing the proportion of variation explained.

Assumptions and limitations

The scatter is constructed to preserve r exactly. The p-value illustrates independent bivariate normal sampling under ρ=0; it is not inference on these artificial points. R² establishes neither causality nor future performance.

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.