Exercise2.3

Question a

data.xyz=UCBAdmissions
summary(data.xyz)
## Number of cases in table: 4526 
## Number of factors: 3 
## Test for independence of all factors:
##  Chisq = 2000.3, df = 16, p-value = 0

The Answer is 4526

Question b

## Dept
##   A   B   C   D   E   F 
## 933 585 918 792 584 714

Question c

data.abc=data.xyz[,1,]+data.xyz[,2,]

Dept A

prop.table(data.abc[,1])
##  Admitted  Rejected 
## 0.6441586 0.3558414

Dept B

prop.table(data.abc[,2])
##  Admitted  Rejected 
## 0.6324786 0.3675214

Dept C

prop.table(data.abc[,3])
##  Admitted  Rejected 
## 0.3507625 0.6492375

Dept D

prop.table(data.abc[,4])
##  Admitted  Rejected 
## 0.3396465 0.6603535

Dept E

prop.table(data.abc[,5])
##  Admitted  Rejected 
## 0.2517123 0.7482877

Dept F

prop.table(data.abc[,6])
##   Admitted   Rejected 
## 0.06442577 0.93557423

Question d

data.123=aperm(data.xyz,c(3,2,1))
prop.table(data.123)
## , , Admit = Admitted
## 
##     Gender
## Dept        Male      Female
##    A 0.113124171 0.019664163
##    B 0.077993814 0.003756076
##    C 0.026513478 0.044631021
##    D 0.030490499 0.028943880
##    E 0.011710119 0.020768891
##    F 0.004860804 0.005302696
## 
## , , Admit = Rejected
## 
##     Gender
## Dept        Male      Female
##    A 0.069155988 0.004197967
##    B 0.045735749 0.001767565
##    C 0.045293858 0.086389748
##    D 0.061643836 0.053910738
##    E 0.030490499 0.066062749
##    F 0.077551922 0.070039770

Exercise 2.5

Question a

data(UKSoccer,package="vcd")
ftable(UKSoccer)
##      Away  0  1  2  3  4
## Home                    
## 0         27 29 10  8  2
## 1         59 53 14 12  4
## 2         28 32 14 12  4
## 3         19 14  7  4  1
## 4          7  8 10  2  0
summary(UKSoccer)
## Number of cases in table: 380 
## Number of factors: 2 
## Test for independence of all factors:
##  Chisq = 18.699, df = 16, p-value = 0.2846
##  Chi-squared approximation may be incorrect

Question b home

home = margin.table(UKSoccer,1)
home
## Home
##   0   1   2   3   4 
##  76 142  90  45  27

away

away = margin.table(UKSoccer,2)
away
## Away
##   0   1   2   3   4 
## 140 136  55  38  11

Question c

dataSoccer=addmargins(UKSoccer)
prop.table(dataSoccer)
##      Away
## Home             0            1            2            3            4
##   0   0.0177631579 0.0190789474 0.0065789474 0.0052631579 0.0013157895
##   1   0.0388157895 0.0348684211 0.0092105263 0.0078947368 0.0026315789
##   2   0.0184210526 0.0210526316 0.0092105263 0.0078947368 0.0026315789
##   3   0.0125000000 0.0092105263 0.0046052632 0.0026315789 0.0006578947
##   4   0.0046052632 0.0052631579 0.0065789474 0.0013157895 0.0000000000
##   Sum 0.0921052632 0.0894736842 0.0361842105 0.0250000000 0.0072368421
##      Away
## Home           Sum
##   0   0.0500000000
##   1   0.0934210526
##   2   0.0592105263
##   3   0.0296052632
##   4   0.0177631579
##   Sum 0.2500000000