The following table shows a study of adolescents of two different age brackets from

three schools on whether they had ever chatted online with someone they did not

know. Data are as shown in the table below.

a$.$ Fit the logit model

$log(\frac{p_{ij}}{1-p_{ij}})={}_0+{}_i^A+{}_j^S+{}_{ij}^{AS}$

where $p_{ij}$ is the probability of an adolescent chatting online with someone they

do not know, A denotes the age of the adolescent, and $S$ denotes the school.

Attach R code used to fit the logit model, and also include summary output for

the model. $(2$ marks$)$

b$.$ Is the model saturated? Why or why not? $(2$ marks$)$

c$.$ Provide a model comparison of this model with the model

$log(\frac{p_{ij}}{1-p_{ij}})={}_0+{}_i^A+{}_j^S$

Write down the hypotheses to be tested, test statistic, distribution of the test

statistic, $p-$value, and conclusion at the $=0\mathrm{.}05$ significance level. $(5$ marks$)$

d$.$ Interpret statistically significant terms $($other than ${}_0)$ for the model presented

in part $($c$)$ using odds ratios $($to $3$dp$),$ and additionally include $95\%$ confidence

intervals $($to $3$dp$)$ for those odds ratios. $(6$ marks$)$Please give this question more detail explanations and answers. thank you!!!