Question

2. 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.), andGENDER (1=male) for 108 individuals. We will be looking for the best set of variables to (parsimoniously?) modelWEIGHT. Even though 6 explanatory variables only gives 2⁹=512 possibilities for “all possible” regressions, we’lltry to be more methodical about it.

##question2
library(MASS)

##
## Attaching package: 'MASS'

## The following object is masked from 'package:olsrr':
##
##     cement

body = read.csv("body.csv", header = T)
attach(body)
chest_diam1  = chest_diam
chest_depth1 = chest_depth
ankle_diam1  = ankle_diam
waist_girth1 = waist_girth
wrist_girth1 = wrist_girth
wrist_diam1  = wrist_diam
age1 = age
height1 = height
gender1= gender
weight1 = weight
detach(body)
bd = data.frame(chest_diam  = chest_diam1,
                chest_depth = chest_depth1,
                ankle_diam  = ankle_diam1,
                waist_girth = waist_girth1,
                wrist_girth = wrist_girth1,
                wrist_diam  = wrist_diam1,

                age = age1,
                height = height1,
                gender = gender1,
                weight = weight1)

attach(bd)

bd.lm = lm(weight ~ ., data = bd)
plot(bd.lm)

body.lm = lm(weight ~ chest_diam + chest_depth + ankle_diam + waist_girth +
               wrist_girth + wrist_diam + age + height + gender, data = body )
summary(body.lm)

##
## Call:
## lm(formula = weight ~ chest_diam + chest_depth + ankle_diam +
##     waist_girth + wrist_girth + wrist_diam + age + height + gender,
##     data = body)
##
## Residuals:
##      Min       1Q   Median       3Q      Max
## -10.5003  -1.7345   0.0929   1.4414   6.8888
##
## Coefficients:
##               Estimate Std. Error t value Pr(>|t|)    
## (Intercept) -119.33349    6.83670 -17.455  < 2e-16 ***
## chest_diam     1.39294    0.21325   6.532 2.91e-09 ***
## chest_depth    0.59732    0.20463   2.919  0.00436 **
## ankle_diam     1.26351    0.44921   2.813  0.00594 **
## waist_girth    0.64234    0.05178  12.404  < 2e-16 ***
## wrist_girth    0.80607    0.42221   1.909  0.05916 .  
## wrist_diam     0.08803    0.55213   0.159  0.87366    
## age           -0.14840    0.03199  -4.639 1.08e-05 ***
## height         0.38080    0.04747   8.022 2.28e-12 ***
## gender        -7.64330    1.12288  -6.807 8.02e-10 ***
## ---
## Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
##
## Residual standard error: 2.75 on 98 degrees of freedom
## Multiple R-squared:  0.9678, Adjusted R-squared:  0.9648
## F-statistic: 327.1 on 9 and 98 DF,  p-value: < 2.2e-16

step_forward = stepAIC(body.lm, direction = "forward")

## Start:  AIC=227.98
## weight ~ chest_diam + chest_depth + ankle_diam + waist_girth +
##     wrist_girth + wrist_diam + age + height + gender

step_forward$anova

## Stepwise Model Path
## Analysis of Deviance Table
##
## Initial Model:
## weight ~ chest_diam + chest_depth + ankle_diam + waist_girth +
##     wrist_girth + wrist_diam + age + height + gender
##
## Final Model:
## weight ~ chest_diam + chest_depth + ankle_diam + waist_girth +
##     wrist_girth + wrist_diam + age + height + gender
##
##
##   Step Df Deviance Resid. Df Resid. Dev      AIC
## 1                         98   740.9312 227.9839

step_backward = stepAIC(body.lm, direction = "backward")

## Start:  AIC=227.98
## weight ~ chest_diam + chest_depth + ankle_diam + waist_girth +
##     wrist_girth + wrist_diam + age + height + gender
##
##               Df Sum of Sq     RSS    AIC
## - wrist_diam   1      0.19  741.12 226.01
## <none>                      740.93 227.98
## - wrist_girth  1     27.56  768.49 229.93
## - ankle_diam   1     59.81  800.75 234.37
## - chest_depth  1     64.42  805.35 234.99
## - age          1    162.71  903.64 247.42
## - chest_diam   1    322.59 1063.52 265.02
## - gender       1    350.30 1091.23 267.80
## - height       1    486.54 1227.47 280.50
## - waist_girth  1   1163.30 1904.23 327.93
##
## Step:  AIC=226.01
## weight ~ chest_diam + chest_depth + ankle_diam + waist_girth +
##     wrist_girth + age + height + gender
##
##               Df Sum of Sq     RSS    AIC
## <none>                      741.12 226.01
## - wrist_girth  1     36.54  777.66 229.21
## - chest_depth  1     64.37  805.49 233.01
## - ankle_diam   1     65.56  806.68 233.17
## - age          1    163.73  904.85 245.57
## - chest_diam   1    328.81 1069.93 263.67
## - gender       1    351.14 1092.26 265.90
## - height       1    486.38 1227.50 278.51
## - waist_girth  1   1215.83 1956.95 328.88

step_backward$anova

## Stepwise Model Path
## Analysis of Deviance Table
##
## Initial Model:
## weight ~ chest_diam + chest_depth + ankle_diam + waist_girth +
##     wrist_girth + wrist_diam + age + height + gender
##
## Final Model:
## weight ~ chest_diam + chest_depth + ankle_diam + waist_girth +
##     wrist_girth + age + height + gender
##
##
##           Step Df  Deviance Resid. Df Resid. Dev      AIC
## 1                                  98   740.9312 227.9839
## 2 - wrist_diam  1 0.1921794        99   741.1234 226.0119

detach(bd)

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

2. Next, use backwards elimination to find the best model for WEIGHT. Give the model. (It may be the same model—noteworthy, either way.)

Finally, as you did in problem 1, fit all possible models, and find the highest adjusted (no need to report the model)- check models wioth 5, 6, and 7 variables.

Answer 1