Homework #1
Jingshu Zhao
2019-07-20
Homework #1 is worth 100 points and each question is worth 6.5 points each.
Submission Instructions: save the .HTML file as ‘HW1_yourlastname.HTML’ and upload the HTML file to the assignment entitled ‘Homework #1’ on Moodle on or before Tuesday July 23, 2019 by 11:55p.m. EST. No late assignments are accepted.
2.1 p.p. 60-61
Run the code chunk below.
library(vcdExtra)## Warning: package 'vcdExtra' was built under R version 3.5.3## Loading required package: vcd## Warning: package 'vcd' was built under R version 3.5.3## Loading required package: grid## Loading required package: gnm## Warning: package 'gnm' was built under R version 3.5.3ds <- datasets(package = c("vcd", "vcdExtra"))
str(ds, vec.len=2)## 'data.frame': 76 obs. of 5 variables:
## $ Package: chr "vcd" "vcd" ...
## $ Item : chr "Arthritis" "Baseball" ...
## $ class : chr "data.frame" "data.frame" ...
## $ dim : chr "84x5" "322x25" ...
## $ Title : chr "Arthritis Treatment Data" "Baseball Data" ...- How many data sets are there altogether? How many are there in each package?
There are 76 data sets altogether. There are 33 data sets in package vcd and 43 data sets in package.
nrow(ds)## [1] 76ds_1 <- datasets(package = "vcd")
nrow(ds_1)## [1] 33ds_2 <- datasets(package = "vcdExtra")
nrow(ds_2)## [1] 43- Make a tabular display of the frequencies by Package and class.
table(ds$Package, ds$class)##
## array data.frame matrix table
## vcd 1 17 0 15
## vcdExtra 3 24 1 15- Choose one or two data sets from this list, and examine their help files (e.g., help(Arthritis) or ?Arthritis). You can use, e.g., example(Arthritis) to run the R code for a given example.
help(Arthritis)## starting httpd help server ... doneexample(Arthritis)##
## Arthrt> data("Arthritis")
##
## Arthrt> art <- xtabs(~ Treatment + Improved, data = Arthritis, subset = Sex == "Female")
##
## Arthrt> art
## Improved
## Treatment None Some Marked
## Placebo 19 7 6
## Treated 6 5 16
##
## Arthrt> mosaic(art, gp = shading_Friendly)
##
## Arthrt> mosaic(art, gp = shading_max)
help(Baseball)
example(Baseball)##
## Basbll> data("Baseball")- p. 61 #2.3
- Find the total number of cases contained in this table. There are total 4526 cases contained in this table
sum(UCBAdmissions)## [1] 4526- For each department, find the total number of applicants.
margin.table(UCBAdmissions,3)## Dept
## A B C D E F
## 933 585 918 792 584 714- For each department, find the overall proportion of applicants who were admitted.
ucb.df <-as.data.frame(UCBAdmissions)
UCB_cont <- xtabs(Freq~Dept + Admit, data = ucb.df)
prop.table(UCB_cont)## Admit
## Dept Admitted Rejected
## A 0.13278833 0.07335395
## B 0.08174989 0.04750331
## C 0.07114450 0.13168361
## D 0.05943438 0.11555457
## E 0.03247901 0.09655325
## F 0.01016350 0.14759169- Construct a tabular display of department (rows) and gender (columns), showing the proportion of applicants in each cell who were admitted relative to the total applicants in that cell.
#total number of student
sum(UCBAdmissions)## [1] 4526#flat table display
flat_ucb <- ftable(Gender ~ Admit + Dept, data = UCBAdmissions)
flat_ucb## Gender Male Female
## Admit Dept
## Admitted A 512 89
## B 353 17
## C 120 202
## D 138 131
## E 53 94
## F 22 24
## Rejected A 313 19
## B 207 8
## C 205 391
## D 279 244
## E 138 299
## F 351 317#proportion of applicants
prop_ucb <- prop.table(flat_ucb)
prop_ucb## Gender Male Female
## Admit Dept
## Admitted 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
## Rejected 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- p. 61 #2.4 a, c, e
- Find the total number of cases represented in this table. There are total 5144 cases represented in this table
sum(DanishWelfare$Freq)## [1] 5144- Convert this data frame to table form, DanishWelfare.tab, a 4-way array containing the frequencies with appropriate variable names and level names.
DanishWelfare.tab <- xtabs(Freq ~., data = DanishWelfare)
str(DanishWelfare.tab)## 'xtabs' num [1:3, 1:4, 1:3, 1:5] 1 3 2 8 1 3 2 5 2 42 ...
## - attr(*, "dimnames")=List of 4
## ..$ Alcohol: chr [1:3] "<1" "1-2" ">2"
## ..$ Income : chr [1:4] "0-50" "50-100" "100-150" ">150"
## ..$ Status : chr [1:3] "Widow" "Married" "Unmarried"
## ..$ Urban : chr [1:5] "Copenhagen" "SubCopenhagen" "LargeCity" "City" ...
## - attr(*, "call")= language xtabs(formula = Freq ~ ., data = DanishWelfare)- Use structable () or ftable () to produce a pleasing flattened display of the frequencies in the 4-way table. Choose the variables used as row and column variables to make it easier to compare levels of Alcohol across the other factors.
ftable(xtabs(Freq ~., data = DanishWelfare))## Urban Copenhagen SubCopenhagen LargeCity City Country
## Alcohol Income Status
## <1 0-50 Widow 1 4 1 8 6
## Married 14 8 41 100 175
## Unmarried 6 1 2 6 9
## 50-100 Widow 8 2 7 14 5
## Married 42 51 62 234 255
## Unmarried 7 5 9 20 27
## 100-150 Widow 2 3 1 5 2
## Married 21 30 23 87 77
## Unmarried 3 2 1 12 4
## >150 Widow 42 29 17 95 46
## Married 24 30 50 167 232
## Unmarried 33 24 15 64 68
## 1-2 0-50 Widow 3 0 1 4 2
## Married 15 7 15 25 48
## Unmarried 2 3 9 9 7
## 50-100 Widow 1 1 3 8 4
## Married 39 59 68 172 143
## Unmarried 12 3 11 20 23
## 100-150 Widow 5 4 1 9 4
## Married 32 68 43 128 86
## Unmarried 6 10 5 21 15
## >150 Widow 26 34 14 48 24
## Married 43 76 70 198 136
## Unmarried 36 23 48 89 64
## >2 0-50 Widow 2 0 2 1 0
## Married 1 2 2 7 7
## Unmarried 3 0 1 5 1
## 50-100 Widow 3 0 2 1 3
## Married 14 21 14 38 35
## Unmarried 2 0 3 12 13
## 100-150 Widow 2 1 1 1 0
## Married 20 31 10 36 21
## Unmarried 0 2 3 9 7
## >150 Widow 21 13 5 20 8
## Married 23 47 21 53 36
## Unmarried 38 20 13 39 26- p. 62 #2.5 a, b, c
#code from text
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- Verify that the total number of games represented in this table is 380.
sum(UKSoccer)## [1] 380# Or use
margin.table(UKSoccer)## [1] 380- Find the marginal total of the number of goals scored by each of the home and away teams.
prop.table(UKSoccer,1)## Away
## Home 0 1 2 3 4
## 0 0.35526316 0.38157895 0.13157895 0.10526316 0.02631579
## 1 0.41549296 0.37323944 0.09859155 0.08450704 0.02816901
## 2 0.31111111 0.35555556 0.15555556 0.13333333 0.04444444
## 3 0.42222222 0.31111111 0.15555556 0.08888889 0.02222222
## 4 0.25925926 0.29629630 0.37037037 0.07407407 0.00000000prop.table(UKSoccer,2)## Away
## Home 0 1 2 3 4
## 0 0.19285714 0.21323529 0.18181818 0.21052632 0.18181818
## 1 0.42142857 0.38970588 0.25454545 0.31578947 0.36363636
## 2 0.20000000 0.23529412 0.25454545 0.31578947 0.36363636
## 3 0.13571429 0.10294118 0.12727273 0.10526316 0.09090909
## 4 0.05000000 0.05882353 0.18181818 0.05263158 0.00000000- Express each of the marginal totals as proportions.
prop.table(margin.table(UKSoccer,1))## Home
## 0 1 2 3 4
## 0.20000000 0.37368421 0.23684211 0.11842105 0.07105263prop.table(margin.table(UKSoccer,2))## Away
## 0 1 2 3 4
## 0.36842105 0.35789474 0.14473684 0.10000000 0.02894737- Run the code below and notice there is a data frame entitled SpaceShuttle. Using the R help, read about the details of this data frame. That is, familiarize yourself with the context and understand the meaning of the different rows.
library(vcd)
library(vcdExtra)
ds <- datasets(package = c("vcd", "vcdExtra"))
str(ds)## 'data.frame': 76 obs. of 5 variables:
## $ Package: chr "vcd" "vcd" "vcd" "vcd" ...
## $ Item : chr "Arthritis" "Baseball" "BrokenMarriage" "Bundesliga" ...
## $ class : chr "data.frame" "data.frame" "data.frame" "data.frame" ...
## $ dim : chr "84x5" "322x25" "20x4" "14018x7" ...
## $ Title : chr "Arthritis Treatment Data" "Baseball Data" "Broken Marriage Data" "Ergebnisse der Fussball-Bundesliga" ...View(ds)
SpaceShuttle## FlightNumber Temperature Pressure Fail nFailures Damage
## 1 1 66 50 no 0 0
## 2 2 70 50 yes 1 4
## 3 3 69 50 no 0 0
## 4 4 80 50 <NA> NA NA
## 5 5 68 50 no 0 0
## 6 6 67 50 no 0 0
## 7 7 72 50 no 0 0
## 8 8 73 50 no 0 0
## 9 9 70 100 no 0 0
## 10 41B 57 100 yes 1 4
## 11 41C 63 200 yes 1 2
## 12 41D 70 200 yes 1 4
## 13 41G 78 200 no 0 0
## 14 51A 67 200 no 0 0
## 15 51C 53 200 yes 2 11
## 16 51D 67 200 no 0 0
## 17 51B 75 200 no 0 0
## 18 51G 70 200 no 0 0
## 19 51F 81 200 no 0 0
## 20 51I 76 200 no 0 0
## 21 51J 79 200 no 0 0
## 22 61A 75 200 yes 2 4
## 23 61C 58 200 yes 1 4
## 24 61I 76 200 no 0 4- Using the structable() function, create a “flat” table that has the Damage Index on the columns and whether the O-ring failed and how many failures on the rows.
structable(Damage ~ Fail + nFailures, data = SpaceShuttle)## Damage 0 2 4 11
## Fail nFailures
## no 0 15 0 1 0
## 1 0 0 0 0
## 2 0 0 0 0
## yes 0 0 0 0 0
## 1 0 1 4 0
## 2 0 0 1 1- Construct the same formatted table that you did in part a, but now use the xtabs() and ftable() functions.
ftable(Damage ~ Fail + nFailures, data = SpaceShuttle)## Damage 0 2 4 11
## Fail nFailures
## no 0 15 0 1 0
## 1 0 0 0 0
## 2 0 0 0 0
## yes 0 0 0 0 0
## 1 0 1 4 0
## 2 0 0 1 1