HHernandez_DATA621_Discussion13

ELMR Exercise 7.1

require("faraway")
library(MASS)
library(ggplot2)
library(dplyr)
library(nnet)

data("hsb")
summary(hsb)

##        id            gender              race         ses    
##  Min.   :  1.00   female:109   african-amer: 20   high  :58  
##  1st Qu.: 50.75   male  : 91   asian       : 11   low   :47  
##  Median :100.50                hispanic    : 24   middle:95  
##  Mean   :100.50                white       :145              
##  3rd Qu.:150.25                                              
##  Max.   :200.00                                              
##      schtyp          prog          read           write      
##  private: 32   academic:105   Min.   :28.00   Min.   :31.00  
##  public :168   general : 45   1st Qu.:44.00   1st Qu.:45.75  
##                vocation: 50   Median :50.00   Median :54.00  
##                               Mean   :52.23   Mean   :52.77  
##                               3rd Qu.:60.00   3rd Qu.:60.00  
##                               Max.   :76.00   Max.   :67.00  
##       math          science          socst      
##  Min.   :33.00   Min.   :26.00   Min.   :26.00  
##  1st Qu.:45.00   1st Qu.:44.00   1st Qu.:46.00  
##  Median :52.00   Median :53.00   Median :52.00  
##  Mean   :52.65   Mean   :51.85   Mean   :52.41  
##  3rd Qu.:59.00   3rd Qu.:58.00   3rd Qu.:61.00  
##  Max.   :75.00   Max.   :74.00   Max.   :71.00

table(hsb$gender, hsb$prog)

##         
##          academic general vocation
##   female       58      24       27
##   male         47      21       23

table(hsb$ses, hsb$prog)

##         
##          academic general vocation
##   high         42       9        7
##   low          19      16       12
##   middle       44      20       31

x <- hsb[,6:11]
cor(x[sapply(x, is.numeric)])

##              read     write      math   science     socst
## read    1.0000000 0.5967765 0.6622801 0.6301579 0.6214843
## write   0.5967765 1.0000000 0.6174493 0.5704416 0.6047932
## math    0.6622801 0.6174493 1.0000000 0.6307332 0.5444803
## science 0.6301579 0.5704416 0.6307332 1.0000000 0.4651060
## socst   0.6214843 0.6047932 0.5444803 0.4651060 1.0000000

# Fit model
mmod <- multinom(prog ~ ., data=x)

## # weights:  21 (12 variable)
## initial  value 219.722458 
## iter  10 value 173.294170
## final  value 164.975567 
## converged

summary(mmod)

## Call:
## multinom(formula = prog ~ ., data = x)
## 
## Coefficients:
##          (Intercept)        read       write        math    science
## general     4.804643 -0.04558434 -0.02299500 -0.09837739 0.09359693
## vocation    9.405865 -0.03583817 -0.03743141 -0.11579827 0.05902499
##                socst
## general  -0.03207906
## vocation -0.06751481
## 
## Std. Errors:
##          (Intercept)       read      write       math    science
## general     1.498368 0.02958174 0.02958054 0.03329584 0.02985794
## vocation    1.621442 0.03205540 0.02955005 0.03639133 0.03026686
##               socst
## general  0.02567748
## vocation 0.02642707
## 
## Residual Deviance: 329.9511 
## AIC: 353.9511

mmod2 <- step(mmod)

## Start:  AIC=353.95
## prog ~ read + write + math + science + socst
## 
## trying - read 
## # weights:  18 (10 variable)
## initial  value 219.722458 
## iter  10 value 172.330870
## final  value 166.302302 
## converged
## trying - write 
## # weights:  18 (10 variable)
## initial  value 219.722458 
## iter  10 value 173.157560
## final  value 165.801985 
## converged
## trying - math 
## # weights:  18 (10 variable)
## initial  value 219.722458 
## iter  10 value 176.402124
## final  value 172.243618 
## converged
## trying - science 
## # weights:  18 (10 variable)
## initial  value 219.722458 
## iter  10 value 180.535654
## final  value 170.511980 
## converged
## trying - socst 
## # weights:  18 (10 variable)
## initial  value 219.722458 
## iter  10 value 174.067882
## final  value 168.411657 
## converged
##           Df      AIC
## - write   10 351.6040
## - read    10 352.6046
## <none>    12 353.9511
## - socst   10 356.8233
## - science 10 361.0240
## - math    10 364.4872
## # weights:  18 (10 variable)
## initial  value 219.722458 
## iter  10 value 173.157560
## final  value 165.801985 
## converged
## 
## Step:  AIC=351.6
## prog ~ read + math + science + socst
## 
## trying - read 
## # weights:  15 (8 variable)
## initial  value 219.722458 
## iter  10 value 167.561494
## final  value 167.337045 
## converged
## trying - math 
## # weights:  15 (8 variable)
## initial  value 219.722458 
## iter  10 value 174.912820
## final  value 174.789964 
## converged
## trying - science 
## # weights:  15 (8 variable)
## initial  value 219.722458 
## iter  10 value 171.176956
## final  value 170.980400 
## converged
## trying - socst 
## # weights:  15 (8 variable)
## initial  value 219.722458 
## iter  10 value 170.918937
## final  value 170.868694 
## converged
##           Df      AIC
## - read     8 350.6741
## <none>    10 351.6040
## - socst    8 357.7374
## - science  8 357.9608
## - math     8 365.5799
## # weights:  15 (8 variable)
## initial  value 219.722458 
## iter  10 value 167.561494
## final  value 167.337045 
## converged
## 
## Step:  AIC=350.67
## prog ~ math + science + socst
## 
## trying - math 
## # weights:  12 (6 variable)
## initial  value 219.722458 
## iter  10 value 180.004472
## final  value 180.004124 
## converged
## trying - science 
## # weights:  12 (6 variable)
## initial  value 219.722458 
## iter  10 value 171.368205
## final  value 171.367391 
## converged
## trying - socst 
## # weights:  12 (6 variable)
## initial  value 219.722458 
## iter  10 value 175.074512
## final  value 175.074335 
## converged
##           Df      AIC
## <none>     8 350.6741
## - science  6 354.7348
## - socst    6 362.1487
## - math     6 372.0082