Data on 173 nesting female horseshoe crabs record for each crab its colour as one of 4 factors (simply labelled $1, \ldots, 4$ ), its width (in $\mathrm{cm}$ ) and the presence of male crabs nearby (a 1 indicating presence). The data are collected into the $\mathrm{R}$ data frame crabs and the first few lines are displayed below.

Describe the model being fitted by the $\mathrm{R}$ command below.

$>$ fit1 <- glm(males colour + width, family = binomial, data=crabs)

The following (abbreviated) output is obtained from the summary command.

Write out the calculation for an approximate $95 \%$ confidence interval for the coefficient for width. Describe the calculation you would perform to obtain an estimate of the probability that a female crab of colour 3 and with a width of $20 \mathrm{~cm}$ has males nearby. [You need not actually compute the end points of the confidence interval or the estimate of the probability above, but merely show the calculations that would need to be performed in order to arrive at them.]