In reading the book "An Introduction to Statistical Learning with Applications in R", I came across this graph:
It shows that the point-wise variance is larger at the ends of the regression curve. Why is that? I thought that the variance may be larger because there seem to be fewer data points near the end, but the variance is calculated on the coefficients so the number of data points used in the estimate has no impact. Then I thought that the variance is larger because the X values are larger, but the graph on the left side shows slight increases in variance on both sides (even when X is small).
In general, I have read that polynomials have notorious end behaviours - what causes this?