\( \newcommand{\bm}[1]{\boldsymbol{\mathbf{#1}}} \DeclareMathOperator{\tr}{tr} \DeclareMathOperator{\var}{var} \DeclareMathOperator{\cov}{cov} \DeclareMathOperator{\corr}{corr} \newcommand{\indep}{\perp\!\!\!\perp} \newcommand{\nindep}{\perp\!\!\!\perp\!\!\!\!\!\!/\;\;} \)

3.3 salinity data

salinity contains \(n = 28\) observations on the salinity of water in Pamlico Sound, North Carolina. The response sal is the bi-weekly average of salinity. The next three columns contain values of the covariates, respectively a lagged value of salinity lag, a trend indicator trend, and the river discharge dis. Using the techniques of the previous problem as a guide, find a model suitable for prediction of salinity from the covariates. The data contain at least one outlier.

(Chapter 8; Ruppert and Carroll, 1980; Atkinson, 1985, p. 48)