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Statistical Modellig

By:   •  March 7, 2019  •  Coursework  •  2,569 Words (11 Pages)  •  30 Views

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Stat Modelling Assignment-3

Varsha

February 28, 2019

Packages Required

library(tidyverse)  #to visualize, transform, input, tidy and join data
library(dplyr)      #data wrangling
library(kableExtra) #to create HTML Table
library(DT)         #to preview the data sets
library(xlsx)       #to load excel files
library(nnet)       #to implement multinomial function

Taking Distance as a multinomial factor

Loaded the datasets and did initial data cleaning(detailed steps were performed in the first assignment)

faa1 <- read.xlsx("FAA1.xls", sheetName = "FAA1")
faa2 <- read.xlsx("FAA2_2.xls", sheetName = "Sheet1")
faa <- bind_rows(faa1, faa2)
check <- faa %>% 
 select(-duration) %>% 
  duplicated() %>% 
  which()

faa <- faa[-check,]

faa_check <- faa %>% 
  filter((duration > 40| is.na(duration)) & (speed_ground >= 30) & (speed_ground <= 140) &
           (height >= 6) & (distance < 6000))
faa <- faa_check

We will create a mulitnomial variabe for distance.

faa1 <- faa %>% 
  mutate(Y = (ifelse(distance < 1000, 1,
                     ifelse( distance >= 1000 & distance < 2000, 2, 3)) ))
faa1$distance <- NULL

Now, we will use multinomial model to fit Y. We treat the new variable Y as categorical under the assumption that the levels of Y have no natural ordering.

faa1$Y <- as.factor(faa1$Y)
faa1 <-  select(faa1, -speed_air ) %>% 
  na.omit()
mmod <- multinom(Y ~ aircraft + duration +
                   no_pasg + speed_ground + pitch + height , faa1)

## # weights:  24 (14 variable)
## initial  value 858.016197
## iter  10 value 581.199724
## iter  20 value 236.239538
## iter  30 value 226.272595
## iter  40 value 226.221087
## iter  50 value 226.174784
## final  value 226.164124
## converged

#summary(mmod)

Based on AIC, we get the model as -

mmodi <- step(mmod)

## Start:  AIC=480.33
## Y ~ aircraft + duration + no_pasg + speed_ground + pitch + height
##
## trying - aircraft
## # weights:  21 (12 variable)
## initial  value 858.016197
## iter  10 value 599.571323
## iter  20 value 336.226736
## iter  30 value 334.049994
## iter  40 value 334.045290
## final  value 334.043139
## converged
## trying - duration
## # weights:  21 (12 variable)
## initial  value 858.016197
## iter  10 value 518.225762
## iter  20 value 239.417331
## iter  30 value 228.258109
## iter  40 value 227.608269
## final  value 227.113768
## converged
## trying - no_pasg
## # weights:  21 (12 variable)
## initial  value 858.016197
## iter  10 value 602.083949
## iter  20 value 240.843149
## iter  30 value 229.631112
## iter  40 value 228.963807
## final  value 228.210500
## converged
## trying - speed_ground
## # weights:  21 (12 variable)
## initial  value 858.016197
## iter  10 value 804.987828
## final  value 794.030499
## converged
## trying - pitch
## # weights:  21 (12 variable)
## initial  value 858.016197
## iter  10 value 582.954258
## iter  20 value 237.697711
## iter  30 value 228.361531
## iter  40 value 227.746783
## final  value 227.327445
## converged
## trying - height
## # weights:  21 (12 variable)
## initial  value 858.016197
## iter  10 value 535.918721
## iter  20 value 302.074403
## iter  30 value 298.921547
## iter  40 value 298.913287
## final  value 298.909431
## converged
##                Df       AIC
## - duration     12  478.2275
## - pitch        12  478.6549
##         14  480.3282
## - no_pasg      12  480.4210
## - height       12  621.8189
## - aircraft     12  692.0863
## - speed_ground 12 1612.0610
## # weights:  21 (12 variable)
## initial  value 858.016197
## iter  10 value 518.225762
## iter  20 value 239.417331
## iter  30 value 228.258109
## iter  40 value 227.608269
## final  value 227.113768
## converged
##
## Step:  AIC=478.23
## Y ~ aircraft + no_pasg + speed_ground + pitch + height
##
## trying - aircraft
## # weights:  18 (10 variable)
## initial  value 858.016197
## iter  10 value 465.319936
## iter  20 value 335.496129
## iter  30 value 335.298663
## final  value 335.293692
## converged
## trying - no_pasg
## # weights:  18 (10 variable)
## initial  value 858.016197
## iter  10 value 444.634863
## iter  20 value 238.604117
## iter  30 value 230.208561
## iter  40 value 229.083783
## iter  40 value 229.083781
## iter  40 value 229.083781
## final  value 229.083781
## converged
## trying - speed_ground
## # weights:  18 (10 variable)
## initial  value 858.016197
## iter  10 value 799.384355
## final  value 796.687299
## converged
## trying - pitch
## # weights:  18 (10 variable)
## initial  value 858.016197
## iter  10 value 488.119245
## iter  20 value 236.788749
## iter  30 value 228.715466
## iter  40 value 228.221740
## final  value 228.220496
## converged
## trying - height
## # weights:  18 (10 variable)
## initial  value 858.016197
## iter  10 value 454.961171
## iter  20 value 300.709209
## iter  30 value 300.281087
## final  value 300.277702
## converged
##                Df       AIC
## - pitch        10  476.4410
## - no_pasg      10  478.1676
##         12  478.2275
## - height       10  620.5554
## - aircraft     10  690.5874
## - speed_ground 10 1613.3746
## # weights:  18 (10 variable)
## initial  value 858.016197
## iter  10 value 488.119245
## iter  20 value 236.788749
## iter  30 value 228.715466
## iter  40 value 228.221740
## final  value 228.220496
## converged
##
## Step:  AIC=476.44
## Y ~ aircraft + no_pasg + speed_ground + height
##
## trying - aircraft
## # weights:  15 (8 variable)
## initial  value 858.016197
## iter  10 value 394.729448
## iter  20 value 347.225190
## iter  30 value 347.118971
## final  value 347.118955
## converged
## trying - no_pasg
## # weights:  15 (8 variable)
## initial  value 858.016197
## iter  10 value 354.469061
## iter  20 value 242.186395
## iter  30 value 231.398332
## final  value 230.124753
## converged
## trying - speed_ground
## # weights:  15 (8 variable)
## initial  value 858.016197
## iter  10 value 797.491849
## final  value 797.489048
## converged
## trying - height
## # weights:  15 (8 variable)
## initial  value 858.016197
## iter  10 value 363.948352
## iter  20 value 301.923434
## iter  30 value 301.017662
## final  value 301.004927
## converged
##                Df       AIC
## - no_pasg       8  476.2495
##         10  476.4410
## - height        8  618.0099
## - aircraft      8  710.2379
## - speed_ground  8 1610.9781
## # weights:  15 (8 variable)
## initial  value 858.016197
## iter  10 value 354.469061
## iter  20 value 242.186395
## iter  30 value 231.398332
## final  value 230.124753
## converged
##
## Step:  AIC=476.25
## Y ~ aircraft + speed_ground + height
##
## trying - aircraft
## # weights:  12 (6 variable)
## initial  value 858.016197
## iter  10 value 378.591341
## iter  20 value 351.025155
## final  value 350.780781
## converged
## trying - speed_ground
## # weights:  12 (6 variable)
## initial  value 858.016197
## iter  10 value 797.741960
## final  value 797.741923
## converged
## trying - height
## # weights:  12 (6 variable)
## initial  value 858.016197
## iter  10 value 345.462031
## iter  20 value 304.390327
## final  value 301.955008
## converged
##                Df       AIC
##          8  476.2495
## - height        6  615.9100
## - aircraft      6  713.5616
## - speed_ground  6 1607.4838

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