Regression: confidence interval and prediction interval

The relationship to understand

Mean CI: ŷ₀±t se√[1/n+(x₀−x̄)²/Sxx]. Individual prediction interval: add 1 inside the square root. se is the residual standard error.

Try it and interpret

For n=20, se=1 and x₀ at the center of the scatter, the half-widths are about 0.47 for the mean and 2.15 for a future observation. Move x₀ beyond the observed range to see the extrapolation warning.

Assumptions and limitations

Simple regression with an intercept and independent normal errors of constant variance. Constructed scatter. Pointwise 95% bands, not simultaneous coverage of the whole curve. Extrapolation may violate the model in ways the band does not measure.

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.