Can anybody explain why confidence bands are closer to the mean in the middle that at the ends?
You can see that in the formulas, but it does make sense.
We have more information near the sample mean, than at x values far from $\displaystyle \bar X$.
For example if x is the age of a person when they can perform some task, then x=0 doesn't make any sense.
Hence a regression line of y(x) really is usless at x=0, but we do want an intercept in our model.
That way we are not forced to go through the origin.
BUT analyzing y at x=0 is pointless, so having a larger variance at x at 0 than at $\displaystyle x=\bar x$ makes sense.
Look at http://www.weibull.com/DOEWeb/confid...regression.htm
when we set $\displaystyle x_-i=\bar x$ the variance term is minimized.
Likewise in the predition intervals