Problem $1$

Use the clouds data from package HSAUR$3$ to build a multiple regression model of the dependent variable

rainfall.

a$)$ Consider all other variables as potential factors in the model $($ this is so called full model$).$

b$)$ Add potential interaction effects if there is any $($use graphical way to help you interpret$).$

c$)$ Remove some non$-$significant variables from the model and compare the new model with the full model.

d$)$ Use the residuals against fitted values of the new mode from c$)$ to check the normality assumption.

Problem $2$

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

mfrow $=c(2,1)$

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

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

Please do each problem and write the code for each in R