Problem $2$

A$)$ compare these two models and write a summary of the findings.

Read the following R codes and the corresponding output then answer the questions.

Model $1$ without interaction

library$($HSAUR$3)$

data$("$womensrole$")$

fm cbind$($agree$,$disagree$)$ ~ gender $+$ education

womensrole$\_$glm glm$($fm$,$ data $=$ womensrole, family $=$ binomial$())$

role.fitted fitted$($womensrole$\_$glm$\_1)$

#role.fitted predict$($womensrole$\_$glm$\_1,$ type $=$ "response"$)$

Plot function

myplot function$($role$.$fitted$)\{$

f womensrole$gender $==$ "Female"

plot$($womensrole$education, role.fitted, type $="$n$",$

ylab $=$ "Probability of agreeing",

xlab $=$ "Education", ylim $=$ c$(0,1))$

lines$($womensrole$education$[!$f$],$ role.fitted$[!$f$],$ lty $=1)$

lines$($womensrole$education$[$f$],$ role.fitted$[$f$],$ lty $=2)$

lgtxt c$("$Fitted $($Males$)",$ "Fitted $($Females$)")$

legend$("$topright$",$ lgtxt$,$ lty $=1$:$2,$ bty $="$n$")$

y womensroleagree $+$

womensrole$disagree$)$

size womensroleagree$+$womensroledisagree

size size $-$ min$($size$)$

size size $/$ max$($size$))*3+1$

text $($womensrole$education$[$f$],$ y$[$f$],"\backslash$VE$",$

family $=$ "HersheySerif", cex $=$ size, col$=$"red"$)$

text$($womensrole$education$[!$f$],$ y$[!$f$],"\backslash$MA$",$

family $=$ "HersheySerif", cex $=$ size, col$=$"blue"$)$

$\}$

Model $2$ with interaction

fm cbind$($agree$,$disagree$)$ ~ gender $*$ education

womensrole$\_$glm glm$($fm$2,$ data $=$ womensrole, family $=$ binomial$())$

role.fitted fitted$($womensrole$\_$glm$\_2)$

Call myplot fuction

par$($mfrow$=$c$(2,1))$

myplot$($role$.$fitted$1)$

myplot$($role$.$fitted$2)$

Figure $1$: the top figure is from model $1$ and bottom figure is from model $2$ with interaction