= Solution
This is a <generalized linear model> with independent <Bernoulli distributions> for the responses and the <logit link>. Under treatment coding with colour one as the reference level, the <linear predictor> is
$$
\log\frac{p_i}{1-p_i}=\beta_0+\beta_2\mathbf1_{\{c_i=2\}}+\beta_3\mathbf1_{\{c_i=3\}}+\beta_4\mathbf1_{\{c_i=4\}}+\beta_w w_i.
$$
Colour is a <categorical variable>, not a numerical trend. Width has the same slope for every colour, since no <interaction term> is fitted. The parameters are estimated by <maximum likelihood estimation>.
The approximate <Wald confidence interval> for the width coefficient is $\boxed{0.46\pm1.96(0.106)}$, or approximately $(0.2522,0.6678)$. This uses the approximate <normal distribution> of the <maximum-likelihood estimator>, rather than a confidence interval for an individual binary response.
For the requested crab, the fitted <linear predictor> is $\widehat\eta=-11.38-0.22+0.46(20)=-2.40$. Applying the inverse <logit link> gives $\boxed{\widehat p=(1+e^{2.40})^{-1}\simeq0.0832}$. The rounded displayed coefficients need not reproduce the reported test statistics exactly.
Back to article page
