The data set $($Canvas: body.csv$)$ contains records of CHEST$\_$DIAM, $,$ CHEST$\_$DEPTH,

ANKLE$\_$DIAM, WAIST$\_$GIRTH, WRIST$\_$GIRTH, WRIST$\_$DIAM $($all in cm$.),$ AGE $($years$),$ WEIGHT

$($kg$.),$ HEIGHT $($cm$.),$ and GENDER $(1=$male$)$ for $108$ individuals. We will be looking for the best set

of variables to $($parsimoniously$?)$ model WEIGHT. Even though $9$ explanatory variables only

gives $29=512$ possibilities for $$all possible$$ regressions, we$$ll try to be more methodical about it$.$

a$.$ First, use forward selection to find the best model for WEIGHT. Give the model.

b$.$ Next, use backwards elimination to find the best model for WEIGHT. Give the model. $($It may

be the same model$$noteworthy$,$ either way.$)$

c$.$ Finally, as you did in problem $1,$ fit all possible models, and find the highest adjusted $2($no

need to report the model$)$check models with $5,6,$ and $7$ variables with the highest adjusted

$2$ compared to yours $($hint$,$ hint$)$is there much difference?##Question $2$

#Load the olsrr library for variable selection processes

library$("$olsrr$")$

#Load the MASS library to iteratively add and remove predictor variables

library$($MASS$)$

#Read the file into the data frame

body $=$ read. csv$("$body$.$csv$",$ header $=T)$

#Attach the 'body' dataframe to make it easier to reference the variables

attach$($body$)$

#Create new variables with a suffix $\text{'}\_$sr$\text{'}($for Step Regression$)$ to keep the original variables for la

chest$\_$diam$\_$sr $=$ chest$\_$diam

chest$\_$depth$\_$sr $=$ chest$\_$depth

Text

ankle$\_$diam$\_$sr $=$ ankle$\_$diam

waist$\_$girth$\_$sr $=$ waist$\_$girth

wrist$\_$girth$\_$sr $=$ wrist$\_$girth

wrist$\_$diam$\_$sr $=$ wrist$\_$diam

age$\_$sr $=$ age

height$\_$sr $=$ height

gender$\_$sr $=$ gender

weight$\_$sr $=$ weight

#Detach the 'body' dataframe to avoid conflicts

detach$($body$)$

#Create a new dataframe 'body$\_$sr$\text{'}$ using the modified variables

body$\_$sr $=$ data.frame$($chest$\_$diam $=$ chest$\_$diam$\_$sr$,$

chest$\_$depth $=$ chest$\_$depth$\_$sr$,$

ankle$\_$diam $=$ ankle$\_$diam$\_$sr$,$

waist$\_$girth $=$ waist$\_$girth$\_$sr$,$

wrist$\_$girth $=$ wrist$\_$girth$\_$sr$,$

wrist$\_$diam $=$ wrist$\_$diam$\_$sr$,$

STA$674-$Assignment $1*$

age $=$ age$\_$sr$,$

height $=$ height$\_$sr$,$

gender $=$ gender$\_$sr$,$

weight $=$ weight$\_$sr$)$

#Attach the 'body$\_$sr$\text{'}$ dataframe for easier reference

attach$($body$\_$sr$)$

#Perform linear regression using the variables in the 'body$\_$sr$\text{'}$ dataframe and plot

body$\_$sr$.$ lm $=$ lm$($weight $.,$ data $=$ body$\_$sr$)$

plot$($body$\_$sr$.$lm$)$

#Perform backward stepwise regression using AIC for model selection

body$\_$sr$.$back $=$ ols$\_$step$\_$backward$\_$aic$($body$\_$sr$.$lm$)$

#Perform forward stepwise regression using AIC for model selection

body$\_$sr$.$forward $=$ ols$\_$step$\_$forward$\_$aic$($body$\_$sr$.$lm$)$

#Plot graphs for the backward and forward stepwise regression model

plot$($body$\_$sr$.$back$)$

plot$($body$\_$sr$.$forward$)$

#Perform linear regression using the variables in the original 'body' dataframe and summarize

body. $lm=$ lm weight $$ chest$\_$diam $+$ chest$\_$depth $+$ ankle$\_$diam $+$ waist$\_$girth $+$

wrist$\_$girth $+$ wrist$\_$diam $+$ age $+$ height $+$ gender, data $=$ body $)$

summary$($body$.$ lm$)$

#Perform backward stepwise regression using AIC and display the ANOVA results

step$\_$backward $=$ stepAIC$($body$.$ lm$,$ direction $=$ "backward"$)$

step$\_$backward$anova

#Perform forward stepwise regression using AIC and display the ANOVA results

step$\_$forward $=$ stepAIC$($body$.lm,$ direction $=$ "forward"$)$

step$\_$forward$anova

#Detach the 'body$\_$sr$\text{'}$ dataframe

detach$($body$\_$sr$)$

STA$674-$Assignment $1*$