Solution (source code)

= Solution

For a model with $k$ fitted parameters and maximized likelihood $L(\widehat\theta)$, the <Akaike information criterion> is
$$
\operatorname{AIC}=-2\log L(\widehat\theta)+2k.
$$
Backward selection starts with the full model, deletes the single variable giving the smallest AIC when that AIC is lower than the current value, and repeats until no deletion improves it. The first deletion is "indus", which gives AIC $1597.8$.