File:part1-fig-09-regression-bands.png

Figure file · Bayesian linear regression

The eight observations, the fitted line, and the two bands. The inner band is for the mean response and the outer for a new observation; the gap between them is the extra 1 in the predictive scale, which is why they never meet however small the leverage term becomes. The vertical rules mark the two predictions computed above, at \widetilde x=4.5 inside the data and \widetilde x=10 beyond it. Both bands are narrowest near \overline x and flare outward, so the cost of extrapolation is a feature of the geometry rather than a separate warning to remember.

The eight observations, the fitted line, and the two bands. The inner band is for the mean response and the outer for a new observation; the gap between them is the extra 1 in the predictive scale, which is why they never meet however small the leverage term becomes. The vertical rules mark the two predictions computed above, at \widetilde x=4.5 inside the data and \widetilde x=10 beyond it. Both bands are narrowest near \overline x and flare outward, so the cost of extrapolation is a feature of the geometry rather than a separate warning to remember.

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Summary

Description. The eight observations, the fitted line, and the two bands. The inner band is for the mean response and the outer for a new observation; the gap between them is the extra 1 in the predictive scale, which is why they never meet however small the leverage term becomes. The vertical rules mark the two predictions computed above, at \widetilde x=4.5 inside the data and \widetilde x=10 beyond it. Both bands are narrowest near \overline x and flare outward, so the cost of extrapolation is a feature of the geometry rather than a separate warning to remember.

Appears in. Bayesian linear regression

Made by. A figure from the course chapter.

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