sec 17.5 (prediction intervals) has issues

[murphyk]

The equation in Sec 17.5.2 (Predicting Crab Size) is likely very obscure to most readers.

Maybe it would be helpful to explain that this is computing the
square root of the variance of the predictive distribution

Var(Y; D) = Var(Y | theta_hat(D)) + Var(theta_hat(D)) 
               ~ sigma_hat^2(D)  + sigma_hat^2(D)/n

(where we treat D as random, since we are adopting the frequentist paradigm).

The equation in sec 17.5.3 (Predicting the Incremental Growth of a Crab) likely looks even more obscure to most readers

It would help to refer back to sec 15.5.1 (A Geometric Problem) where you have a (very elegant) derivation
of theta_hat = (X' X)^{-1} X' y and also mention that sigma_hat = SD(e). Then maybe explain what you computing is the square root of the variance of the conditional predictive distribution

Var(Y0|x0; D) = Var(Y0 | x0; theta_hat(D)) + Var(theta_hat(D) | x0) 
                     ~ sigma_hat^2(D) + sigma_hat^2(D) x_0' (X' X)^{-1} x_0

(where we treat D=(X,y) as random, and x0 as fixed). (I have assumed x0 is a column vector, rather than a row vector, so that the second term looks like an inner product, as it should.)

You can then explain that these equations are derived in sec 17.6 (I assume...)