In-class exercises:
1.Split the ChickWeight{datasets} data by individual chicks to extract separate slope estimates of regressing weight onto Time for each chick.
dta <- ChickWeight
str(dta)
#> Classes 'nfnGroupedData', 'nfGroupedData', 'groupedData' and 'data.frame': 578 obs. of 4 variables:
#> $ weight: num 42 51 59 64 76 93 106 125 149 171 ...
#> $ Time : num 0 2 4 6 8 10 12 14 16 18 ...
#> $ Chick : Ord.factor w/ 50 levels "18"<"16"<"15"<..: 15 15 15 15 15 15 15 15 15 15 ...
#> $ Diet : Factor w/ 4 levels "1","2","3","4": 1 1 1 1 1 1 1 1 1 1 ...
#> - attr(*, "formula")=Class 'formula' language weight ~ Time | Chick
#> .. ..- attr(*, ".Environment")=<environment: R_EmptyEnv>
#> - attr(*, "outer")=Class 'formula' language ~Diet
#> .. ..- attr(*, ".Environment")=<environment: R_EmptyEnv>
#> - attr(*, "labels")=List of 2
#> ..$ x: chr "Time"
#> ..$ y: chr "Body weight"
#> - attr(*, "units")=List of 2
#> ..$ x: chr "(days)"
#> ..$ y: chr "(gm)"
dim(dta)
#> [1] 578 4
head(dta)
#> weight Time Chick Diet
#> 1 42 0 1 1
#> 2 51 2 1 1
#> 3 59 4 1 1
#> 4 64 6 1 1
#> 5 76 8 1 1
#> 6 93 10 1 1
dta2 <- lapply(split(dta[, 1:2], list(dta$Chick)), function(x) lm(weight~Time, data = x))
sapply(dta2, coef)
#> 18 16 15 13 9 20 10
#> (Intercept) 39 43.392857 46.83333 43.384359 52.094086 37.667826 38.695054
#> Time -2 1.053571 1.89881 2.239601 2.663137 3.732718 4.066102
#> 8 17 19 4 6 11 3
#> (Intercept) 43.727273 43.030706 31.21222 32.86568 44.123431 47.921948 23.17955
#> Time 4.827273 4.531538 5.08743 6.08864 6.378006 7.510967 8.48737
#> 1 12 2 5 14 7 24
#> (Intercept) 24.465436 21.939797 24.724853 16.89563 20.52488 5.842535 53.067766
#> Time 7.987899 8.440629 8.719861 10.05536 11.98245 13.205264 1.207533
#> 30 22 23 27 28 26 25
#> (Intercept) 39.109666 40.082590 38.428074 29.858569 23.984874 20.70715 19.65119
#> Time 5.898351 5.877931 6.685978 7.379368 9.703676 10.10316 11.30676
#> 29 21 33 37 36 31 39
#> (Intercept) 5.882771 15.56330 45.830283 29.608834 25.85403 19.13099 17.03661
#> Time 12.453487 15.47512 5.855241 6.677053 9.99047 10.02617 10.73710
#> 38 32 40 34 35 44 45
#> (Intercept) 10.67282 13.69173 10.83830 5.081682 4.757979 44.909091 35.673121
#> Time 12.06051 13.18091 13.44229 15.000151 17.258811 6.354545 7.686432
#> 43 41 47 49 46 50 42
#> (Intercept) 52.185751 39.337922 36.489790 31.662986 27.771744 23.78218 19.86507
#> Time 8.318863 8.159885 8.374981 9.717894 9.738466 11.33293 11.83679
#> 48
#> (Intercept) 7.947663
#> Time 13.7147182.Explain what does this statement do: lapply(lapply(search(), ls), length)
lapply(lapply(search(), ls), length)
#> [[1]]
#> [1] 2
#>
#> [[2]]
#> [1] 449
#>
#> [[3]]
#> [1] 87
#>
#> [[4]]
#> [1] 113
#>
#> [[5]]
#> [1] 245
#>
#> [[6]]
#> [1] 104
#>
#> [[7]]
#> [1] 203
#>
#> [[8]]
#> [1] 0
#>
#> [[9]]
#> [1] 1246
#重複使用索引值來擷取資料，這裡lapply會將運算公式代入到輸入檔案的每個元素上#3.The following R script uses Cushings{MASS} to demonstrates several ways to achieve the same objective in R. Explain the advantages or disadvantages of each method.
#
# Cushings example
#
library(pacman)
pacman::p_load(MASS, tidyverse)
# method 1：最短最簡單，直接生成list類型的資料
M1 <- aggregate( . ~ Type, data = Cushings, mean)
mode(M1)
#> [1] "list"
M1
#> Type Tetrahydrocortisone Pregnanetriol
#> 1 a 2.966667 2.44
#> 2 b 8.180000 1.12
#> 3 c 19.720000 5.50
#> 4 u 14.016667 1.20
# method 2：長了一點，生成的是numeric類型的資料
M2 <- sapply(split(Cushings[,-3], Cushings$Type), function(x) apply(x, 2, mean))
mode(M2)
#> [1] "numeric"
M2
#> a b c u
#> Tetrahydrocortisone 2.966667 8.18 19.72 14.01667
#> Pregnanetriol 2.440000 1.12 5.50 1.20000
# method 3：看起來比較亂，生成的是numeric類型的資料
M3 <- do.call("rbind", as.list(
by(Cushings, list(Cushings$Type), function(x) {
y <- subset(x, select = -Type)
apply(y, 2, mean)
}
)))
mode(M3)
#> [1] "numeric"
M3
#> Tetrahydrocortisone Pregnanetriol
#> a 2.966667 2.44
#> b 8.180000 1.12
#> c 19.720000 5.50
#> u 14.016667 1.20
# method 4:使用運算子較簡單，生成list類型的資料
M4 <- Cushings %>%
group_by(Type) %>%
summarize( t_m = mean(Tetrahydrocortisone), p_m = mean(Pregnanetriol))
mode(M4)
#> [1] "list"
M4
#> # A tibble: 4 x 3
#> Type t_m p_m
#> <fct> <dbl> <dbl>
#> 1 a 2.97 2.44
#> 2 b 8.18 1.12
#> 3 c 19.7 5.5
#> 4 u 14.0 1.2
# method 5：使用運算子較簡單，但是比上面繁複，生成list類型的資料
M5 <- Cushings %>%
nest(-Type) %>%
mutate(avg = map(data, ~ apply(., 2, mean)),
res_1 = map_dbl(avg, "Tetrahydrocortisone"),
res_2 = map_dbl(avg, "Pregnanetriol"))
#> Warning: All elements of `...` must be named.
#> Did you want `data = c(Tetrahydrocortisone, Pregnanetriol)`?
mode(M5)
#> [1] "list"
M5
#> # A tibble: 4 x 5
#> Type data avg res_1 res_2
#> <fct> <list> <list> <dbl> <dbl>
#> 1 a <tibble [6 x 2]> <dbl [2]> 2.97 2.44
#> 2 b <tibble [10 x 2]> <dbl [2]> 8.18 1.12
#> 3 c <tibble [5 x 2]> <dbl [2]> 19.7 5.5
#> 4 u <tibble [6 x 2]> <dbl [2]> 14.0 1.2
###4.Go through the script in the NZ schools example and provide comments to each code chunk indicated by ‘##’. Give alternative code to perform the same calculation where appropriate.
#
# a case study
#
#將dta定義為nzSchools.csv這個檔案# keep the school names with white spaces
dta <- read.csv("C:/Users/boss/Desktop/data_management/nzSchools.csv", as.is=2)
#看這個檔案的結構#
str(dta)
#> 'data.frame': 2571 obs. of 6 variables:
#> $ ID : int 1015 1052 1062 1092 1130 1018 1029 1030 1588 1154 ...
#> $ Name: chr "Hora Hora School" "Morningside School" "Onerahi School" "Raurimu Avenue School" ...
#> $ City: Factor w/ 541 levels "Ahaura","Ahipara",..: 533 533 533 533 533 533 533 533 533 533 ...
#> $ Auth: Factor w/ 4 levels "Other","Private",..: 3 3 3 3 3 3 3 3 4 3 ...
#> $ Dec : int 2 3 4 2 4 8 5 5 6 1 ...
#> $ Roll: int 318 200 455 86 577 329 637 395 438 201 ...
#看這檔案的行列數量#
dim(dta)
#> [1] 2571 6
#分箱# binning
#將dta$Size定義為如果在資料中"Roll"這一欄大於median的不是歸於"Large"就是歸於"Small"#
dta$Size <- ifelse(dta$Roll > median(dta$Roll), "Large", "Small")
#將dta$size指定為空值#
dta$Size <- NULL
#再看一次檔案#
head(dta)
#> ID Name City Auth Dec Roll
#> 1 1015 Hora Hora School Whangarei State 2 318
#> 2 1052 Morningside School Whangarei State 3 200
#> 3 1062 Onerahi School Whangarei State 4 455
#> 4 1092 Raurimu Avenue School Whangarei State 2 86
#> 5 1130 Whangarei School Whangarei State 4 577
#> 6 1018 Hurupaki School Whangarei State 8 329
#將dta$Size再次指定為將Roll分割成"Small", "Mediam", "Large"3欄#
dta$Size <- cut(dta$Roll, 3, labels=c("Small", "Mediam", "Large"))
#將dta$ssize單獨拿出來看，發現照著"Small", "Mediam", "Large"的順序排在其下有多少筆資料#
table(dta$Size)
#>
#> Small Mediam Large
#> 2555 15 1
#分類# sorting
#將dta$RollOrdg定義為dta$Roll照著降冪排欄#
dta$RollOrd <- order(dta$Roll, decreasing=T)
#看前面6筆數據#
head(dta[dta$RollOrd, ])
#> ID Name City Auth Dec Roll Size RollOrd
#> 1726 498 Correspondence School Wellington State NA 5546 Large 753
#> 301 28 Rangitoto College Auckland State 10 3022 Mediam 353
#> 376 78 Avondale College Auckland State 4 2613 Mediam 712
#> 2307 319 Burnside High School Christchurch State 8 2588 Mediam 709
#> 615 41 Macleans College Auckland State 10 2476 Mediam 1915
#> 199 43 Massey High School Auckland State 5 2452 Mediam 1683
#看後面6筆數據#
tail(dta[dta$RollOrd, ])
#> ID Name City Auth Dec Roll Size
#> 2401 1641 Amana Christian School Dunedin Private 9 7 Small
#> 1590 2461 Tangimoana School Manawatu State 4 6 Small
#> 1996 3598 Woodbank School Kaikoura State 4 6 Small
#> 2112 3386 Jacobs River School Jacobs River State 5 6 Small
#> 1514 2407 Ngamatapouri School Sth Taranaki District State 9 5 Small
#> 1575 2420 Papanui Junction School Taihape State 5 5 Small
#> RollOrd
#> 2401 2562
#> 1590 266
#> 1996 2478
#> 2112 1501
#> 1514 2377
#> 1575 1542
#除了dta$Roll照著降冪排欄以外，加上照著City欄排好，並看前面6筆數據#
head(dta[order(dta$City, dta$Roll, decreasing=T), ])
#> ID Name City Auth Dec Roll Size RollOrd
#> 2548 401 Menzies College Wyndham State 4 356 Small 859
#> 2549 4054 Wyndham School Wyndham State 5 94 Small 1163
#> 1611 2742 Woodville School Woodville State 3 147 Small 726
#> 1630 2640 Papatawa School Woodville State 7 27 Small 2273
#> 2041 3600 Woodend School Woodend State 9 375 Small 1401
#> 1601 399 Central Southland College Winton State 7 549 Small 450
#除了dta$Roll照著降冪排欄以外，加上照著City欄排好，並看後面6筆數據#
tail(dta[order(dta$City, dta$Roll, decreasing=T), ])
#> ID Name City Auth Dec Roll Size RollOrd
#> 2169 3273 Albury School Albury State 8 30 Small 1010
#> 2018 350 Akaroa Area School Akaroa State 8 125 Small 1051
#> 2023 3332 Duvauchelle School Akaroa State 9 41 Small 749
#> 335 1200 Ahuroa School Ahuroa State 7 22 Small 193
#> 99 1000 Ahipara School Ahipara State 3 241 Small 1963
#> 2117 2105 Awahono School - Grey Valley Ahaura State 4 119 Small 364
#計數# counting
#看Auth這一欄下的數據#
table(dta$Auth)
#>
#> Other Private State State Integrated
#> 1 99 2144 327
#將authtbl定義為Auth這一欄下的數據，並打開來看#
authtbl <- table(dta$Auth); authtbl
#>
#> Other Private State State Integrated
#> 1 99 2144 327
#看authtbl資料屬性為table#
class(authtbl)
#> [1] "table"
#將Auth2以下屬於other的資料調出來看#
dta[dta$Auth == "Other", ]
#> ID Name City Auth Dec Roll Size RollOrd
#> 2315 518 Kingslea School Christchurch Other 1 51 Small 1579
#將行設定為Auth欄位資料，將欄設為Dec資料，做交叉表#
xtabs(~ Auth + Dec, data=dta)
#> Dec
#> Auth 1 2 3 4 5 6 7 8 9 10
#> Other 1 0 0 0 0 0 0 0 0 0
#> Private 0 0 2 6 2 2 6 11 12 38
#> State 259 230 208 219 214 215 188 200 205 205
#> State Integrated 12 22 35 28 38 34 45 45 37 31
#匯總# aggregating
#計算Roll欄位底下數據的平均數#
mean(dta$Roll)
#> [1] 295.4737
#計算Roll欄位底下數據以及Auth底下"Private"欄位數據的平均數#
mean(dta$Roll[dta$Auth == "Private"])
#> [1] 308.798
#匯總資料內"Roll"欄位的數據並分別照dta$Auth的分類計算平均數#
aggregate(dta["Roll"], by=list(dta$Auth), FUN=mean)
#> Group.1 Roll
#> 1 Other 51.0000
#> 2 Private 308.7980
#> 3 State 300.6301
#> 4 State Integrated 258.3792
#將dta$Rich定義為資料內Dec欄位的資料若大於5顯示為True，再看此定義資料#
dta$Rich <- dta$Dec > 5; dta$Rich
#> [1] FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE TRUE FALSE FALSE FALSE
#> [13] FALSE FALSE FALSE FALSE FALSE TRUE FALSE FALSE FALSE FALSE TRUE TRUE
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#> [2077] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
#> [2089] TRUE FALSE FALSE FALSE FALSE TRUE FALSE TRUE FALSE FALSE TRUE FALSE
#> [2101] TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE NA FALSE FALSE
#> [2113] FALSE TRUE TRUE TRUE FALSE TRUE FALSE FALSE FALSE TRUE FALSE FALSE
#> [2125] TRUE FALSE TRUE TRUE TRUE FALSE TRUE TRUE FALSE TRUE FALSE FALSE
#> [2137] TRUE TRUE FALSE TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE
#> [2149] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE FALSE FALSE TRUE TRUE
#> [2161] TRUE TRUE TRUE TRUE TRUE FALSE TRUE FALSE TRUE TRUE FALSE TRUE
#> [2173] FALSE TRUE FALSE FALSE TRUE FALSE FALSE TRUE TRUE TRUE TRUE TRUE
#> [2185] TRUE TRUE TRUE TRUE FALSE TRUE FALSE TRUE TRUE TRUE FALSE FALSE
#> [2197] FALSE FALSE TRUE TRUE FALSE TRUE FALSE TRUE TRUE FALSE TRUE TRUE
#> [2209] FALSE FALSE TRUE TRUE TRUE TRUE TRUE FALSE TRUE FALSE FALSE FALSE
#> [2221] FALSE TRUE TRUE FALSE TRUE FALSE FALSE FALSE TRUE TRUE TRUE FALSE
#> [2233] TRUE TRUE FALSE TRUE FALSE FALSE TRUE FALSE TRUE TRUE TRUE FALSE
#> [2245] FALSE FALSE FALSE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
#> [2257] FALSE TRUE FALSE FALSE TRUE FALSE TRUE FALSE FALSE FALSE FALSE FALSE
#> [2269] FALSE TRUE TRUE FALSE TRUE TRUE TRUE TRUE FALSE FALSE FALSE TRUE
#> [2281] TRUE TRUE TRUE TRUE FALSE FALSE TRUE TRUE TRUE TRUE TRUE FALSE
#> [2293] FALSE TRUE FALSE TRUE FALSE FALSE FALSE FALSE TRUE FALSE TRUE TRUE
#> [2305] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE FALSE FALSE TRUE
#> [2317] TRUE FALSE FALSE FALSE FALSE FALSE FALSE TRUE TRUE FALSE FALSE TRUE
#> [2329] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE FALSE TRUE TRUE
#> [2341] TRUE TRUE FALSE FALSE FALSE TRUE TRUE FALSE FALSE FALSE FALSE FALSE
#> [2353] TRUE FALSE FALSE TRUE FALSE TRUE FALSE TRUE TRUE TRUE TRUE FALSE
#> [2365] TRUE TRUE TRUE FALSE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
#> [2377] TRUE TRUE FALSE TRUE FALSE FALSE TRUE TRUE TRUE TRUE TRUE FALSE
#> [2389] TRUE TRUE TRUE TRUE FALSE TRUE FALSE TRUE TRUE FALSE TRUE TRUE
#> [2401] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
#> [2413] TRUE FALSE FALSE FALSE FALSE FALSE FALSE TRUE TRUE TRUE TRUE FALSE
#> [2425] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
#> [2437] TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
#> [2449] TRUE FALSE FALSE FALSE TRUE TRUE FALSE TRUE TRUE TRUE TRUE TRUE
#> [2461] TRUE TRUE TRUE TRUE TRUE TRUE TRUE FALSE TRUE FALSE FALSE TRUE
#> [2473] TRUE FALSE TRUE TRUE TRUE FALSE TRUE TRUE TRUE TRUE TRUE TRUE
#> [2485] TRUE TRUE FALSE FALSE FALSE FALSE TRUE TRUE TRUE TRUE TRUE FALSE
#> [2497] TRUE FALSE TRUE TRUE FALSE FALSE TRUE TRUE TRUE TRUE TRUE TRUE
#> [2509] TRUE TRUE TRUE TRUE TRUE TRUE FALSE TRUE TRUE TRUE TRUE TRUE
#> [2521] TRUE FALSE FALSE FALSE TRUE FALSE TRUE TRUE TRUE TRUE TRUE FALSE
#> [2533] TRUE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE FALSE TRUE
#> [2545] FALSE FALSE TRUE FALSE FALSE FALSE TRUE FALSE TRUE TRUE FALSE TRUE
#> [2557] FALSE TRUE FALSE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE TRUE
#> [2569] FALSE TRUE TRUE
#匯總資料內"Roll"欄位的數據並分別照dta$Auth以及dta$Rich的分類計算平均數#
aggregate(dta["Roll"], by=list(dta$Auth, dta$Rich), FUN=mean)
#> Group.1 Group.2 Roll
#> 1 Other FALSE 51.0000
#> 2 Private FALSE 151.4000
#> 3 State FALSE 261.7487
#> 4 State Integrated FALSE 183.2370
#> 5 Private TRUE 402.5362
#> 6 State TRUE 338.8243
#> 7 State Integrated TRUE 311.2135
#匯總資料內"Roll"欄位的數據並照dta$Auth的分類計算上下限#
by(dta["Roll"], INDICES=list(dta$Auth), FUN=range)
#> : Other
#> [1] 51 51
#> ------------------------------------------------------------
#> : Private
#> [1] 7 1663
#> ------------------------------------------------------------
#> : State
#> [1] 5 5546
#> ------------------------------------------------------------
#> : State Integrated
#> [1] 18 1475
###5.Go through the script in the NCEA 2007 example and provide comments to each code chunk indicated by ‘##’. Give alternative code to perform the same calculation where appropriate.
#
# a case study - II #
#開檔案#
dta2 <- read.table("C:/Users/boss/Desktop/data_management/NCEA2007.txt", sep=":", quote="", h=T, as.is=T)
#看這檔案的行列數量#
dim(dta2)
#> [1] 88 4
#看這個檔案的結構#
str(dta2)
#> 'data.frame': 88 obs. of 4 variables:
#> $ Name : chr "Al-Madinah School" "Alfriston College" "Ambury Park Centre for Riding Therapy" "Aorere College" ...
#> $ Level1: num 61.5 53.9 33.3 39.5 71.2 22.1 50.8 57.3 89.3 59.8 ...
#> $ Level2: num 75 44.1 20 50.2 78.9 30.8 34.8 49.8 89.7 65.7 ...
#> $ Level3: num 0 0 0 30.6 55.5 26.3 48.9 44.6 88.6 50.4 ...
#看這個檔案前6筆數據#
head(dta2)
#> Name Level1 Level2 Level3
#> 1 Al-Madinah School 61.5 75.0 0.0
#> 2 Alfriston College 53.9 44.1 0.0
#> 3 Ambury Park Centre for Riding Therapy 33.3 20.0 0.0
#> 4 Aorere College 39.5 50.2 30.6
#> 5 Auckland Girls' Grammar School 71.2 78.9 55.5
#> 6 Auckland Grammar 22.1 30.8 26.3
#計算這個檔案中，每一欄全部數據加總的平均數#
apply(dta2[, -1], MARGIN=2, FUN=mean)
#> Level1 Level2 Level3
#> 62.26705 61.06818 47.97614
#計算這個檔案中，每一欄全部數據加總的平均數，然後apply回來一個list給你# list apply
lapply(dta2[, -1], FUN=mean)
#> $Level1
#> [1] 62.26705
#>
#> $Level2
#> [1] 61.06818
#>
#> $Level3
#> [1] 47.97614
#計算這個檔案中，每一欄全部數據加總的平均數，然後apply回來一個向量數據給你# simplify the list apply
sapply(dta2[, -1], FUN=mean)
#> Level1 Level2 Level3
#> 62.26705 61.06818 47.97614
#計算這個檔案中，每一欄全部數據的最大與最小值#
apply(dta2[, -1], MARGIN=2, FUN=range)
#> Level1 Level2 Level3
#> [1,] 2.8 0.0 0.0
#> [2,] 97.4 95.7 95.7
#計算這個檔案中，每一欄全部數據的最大與最小值，然後apply回來一個list給你#
lapply(dta2[, -1], FUN=range)
#> $Level1
#> [1] 2.8 97.4
#>
#> $Level2
#> [1] 0.0 95.7
#>
#> $Level3
#> [1] 0.0 95.7
#計算這個檔案中，每一欄全部數據的最大與最小值，然後apply回來一個向量數據給你#
sapply(dta2[, -1], FUN=range)
#> Level1 Level2 Level3
#> [1,] 2.8 0.0 0.0
#> [2,] 97.4 95.7 95.7
#分割# splitting
#將rollsByAuth定義為將檔案切割成：行以Roll的欄位，欄以AUth的欄位，做成一個表格#
rollsByAuth <- split(dta$Roll, dta$Auth)
#看這個表格#
str(rollsByAuth)
#> List of 4
#> $ Other : int 51
#> $ Private : int [1:99] 255 39 154 73 83 25 95 85 94 729 ...
#> $ State : int [1:2144] 318 200 455 86 577 329 637 395 201 267 ...
#> $ State Integrated: int [1:327] 438 26 191 560 151 114 126 171 211 57 ...
#這個矩陣的表格屬性是list#
class(rollsByAuth)
#> [1] "list"
#計算每一行的平均數，並給你一個list#
lapply(split(dta$Roll, dta$Auth), mean)
#> $Other
#> [1] 51
#>
#> $Private
#> [1] 308.798
#>
#> $State
#> [1] 300.6301
#>
#> $`State Integrated`
#> [1] 258.3792
#計算每一行的平均數，並給你一個向量數據#
sapply(split(dta$Roll, dta$Auth), mean)
#> Other Private State State Integrated
#> 51.0000 308.7980 300.6301 258.3792
###Exercises:
1.Use the data in the high schools example to solve the following problems:
test if any pairs of the five variables: read, write, math, science, and socst, are different in means.
test if the 4 different ethnic groups have the same mean scores for each of the 5 variables (individually): read, write, math, science, and socst.
Perform all pairwise simple regressions for these variables: read, write, math, science, and socst.
dta <- read.table("C:/Users/boss/Desktop/data_management/hs0.txt", h=T)
str(dta)
#> 'data.frame': 200 obs. of 11 variables:
#> $ id : int 70 121 86 141 172 113 50 11 84 48 ...
#> $ female : chr "male" "female" "male" "male" ...
#> $ race : chr "white" "white" "white" "white" ...
#> $ ses : chr "low" "middle" "high" "high" ...
#> $ schtyp : chr "public" "public" "public" "public" ...
#> $ prog : chr "general" "vocation" "general" "vocation" ...
#> $ read : int 57 68 44 63 47 44 50 34 63 57 ...
#> $ write : int 52 59 33 44 52 52 59 46 57 55 ...
#> $ math : int 41 53 54 47 57 51 42 45 54 52 ...
#> $ science: int 47 63 58 53 53 63 53 39 58 NA ...
#> $ socst : int 57 61 31 56 61 61 61 36 51 51 ...
head(dta)
#> id female race ses schtyp prog read write math science socst
#> 1 70 male white low public general 57 52 41 47 57
#> 2 121 female white middle public vocation 68 59 53 63 61
#> 3 86 male white high public general 44 33 54 58 31
#> 4 141 male white high public vocation 63 44 47 53 56
#> 5 172 male white middle public academic 47 52 57 53 61
#> 6 113 male white middle public academic 44 52 51 63 61
dim(dta)
#> [1] 200 11
mode(dta)
#> [1] "list"
class(dta)
#> [1] "data.frame"
#(a)
dta2 <- stack(dta[, c(7:11)])
dta2
#> values ind
#> 1 57 read
#> 2 68 read
#> 3 44 read
#> 4 63 read
#> 5 47 read
#> 6 44 read
#> 7 50 read
#> 8 34 read
#> 9 63 read
#> 10 57 read
#> 11 60 read
#> 12 57 read
#> 13 73 read
#> 14 54 read
#> 15 45 read
#> 16 42 read
#> 17 47 read
#> 18 57 read
#> 19 68 read
#> 20 55 read
#> 21 63 read
#> 22 63 read
#> 23 50 read
#> 24 60 read
#> 25 37 read
#> 26 34 read
#> 27 65 read
#> 28 47 read
#> 29 44 read
#> 30 52 read
#> 31 42 read
#> 32 76 read
#> 33 65 read
#> 34 42 read
#> 35 52 read
#> 36 60 read
#> 37 68 read
#> 38 65 read
#> 39 47 read
#> 40 39 read
#> 41 47 read
#> 42 55 read
#> 43 52 read
#> 44 42 read
#> 45 65 read
#> 46 55 read
#> 47 50 read
#> 48 65 read
#> 49 47 read
#> 50 57 read
#> 51 53 read
#> 52 39 read
#> 53 44 read
#> 54 63 read
#> 55 73 read
#> 56 39 read
#> 57 37 read
#> 58 42 read
#> 59 63 read
#> 60 48 read
#> 61 50 read
#> 62 47 read
#> 63 44 read
#> 64 34 read
#> 65 50 read
#> 66 44 read
#> 67 60 read
#> 68 47 read
#> 69 63 read
#> 70 50 read
#> 71 44 read
#> 72 60 read
#> 73 73 read
#> 74 68 read
#> 75 55 read
#> 76 47 read
#> 77 55 read
#> 78 68 read
#> 79 31 read
#> 80 47 read
#> 81 63 read
#> 82 36 read
#> 83 68 read
#> 84 63 read
#> 85 55 read
#> 86 55 read
#> 87 52 read
#> 88 34 read
#> 89 50 read
#> 90 55 read
#> 91 52 read
#> 92 63 read
#> 93 68 read
#> 94 39 read
#> 95 44 read
#> 96 50 read
#> 97 71 read
#> 98 63 read
#> 99 34 read
#> 100 63 read
#> 101 68 read
#> 102 47 read
#> 103 47 read
#> 104 63 read
#> 105 52 read
#> 106 55 read
#> 107 60 read
#> 108 35 read
#> 109 47 read
#> 110 71 read
#> 111 57 read
#> 112 44 read
#> 113 65 read
#> 114 68 read
#> 115 73 read
#> 116 36 read
#> 117 43 read
#> 118 73 read
#> 119 52 read
#> 120 41 read
#> 121 60 read
#> 122 50 read
#> 123 50 read
#> 124 47 read
#> 125 47 read
#> 126 55 read
#> 127 50 read
#> 128 39 read
#> 129 50 read
#> 130 34 read
#> 131 57 read
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#> 133 68 read
#> 134 42 read
#> 135 61 read
#> 136 76 read
#> 137 47 read
#> 138 46 read
#> 139 39 read
#> 140 52 read
#> 141 28 read
#> 142 42 read
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#> 147 50 read
#> 148 44 read
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#> 152 65 read
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#> 154 47 read
#> 155 57 read
#> 156 68 read
#> 157 52 read
#> 158 42 read
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#> 160 66 read
#> 161 47 read
#> 162 57 read
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#> 165 52 read
#> 166 44 read
#> 167 50 read
#> 168 39 read
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#> 171 42 read
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#> 173 42 read
#> 174 60 read
#> 175 44 read
#> 176 63 read
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#> 179 50 read
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#> 181 60 read
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#> 184 55 read
#> 185 50 read
#> 186 65 read
#> 187 52 read
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#> 189 63 read
#> 190 50 read
#> 191 42 read
#> 192 36 read
#> 193 50 read
#> 194 41 read
#> 195 47 read
#> 196 55 read
#> 197 42 read
#> 198 57 read
#> 199 55 read
#> 200 63 read
#> 201 52 write
#> 202 59 write
#> 203 33 write
#> 204 44 write
#> 205 52 write
#> 206 52 write
#> 207 59 write
#> 208 46 write
#> 209 57 write
#> 210 55 write
#> 211 46 write
#> 212 65 write
#> 213 60 write
#> 214 63 write
#> 215 57 write
#> 216 49 write
#> 217 52 write
#> 218 57 write
#> 219 65 write
#> 220 39 write
#> 221 49 write
#> 222 63 write
#> 223 40 write
#> 224 52 write
#> 225 44 write
#> 226 37 write
#> 227 65 write
#> 228 57 write
#> 229 38 write
#> 230 44 write
#> 231 31 write
#> 232 52 write
#> 233 67 write
#> 234 41 write
#> 235 59 write
#> 236 65 write
#> 237 54 write
#> 238 62 write
#> 239 31 write
#> 240 31 write
#> 241 47 write
#> 242 59 write
#> 243 54 write
#> 244 41 write
#> 245 65 write
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#> 247 40 write
#> 248 59 write
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#> 250 54 write
#> 251 61 write
#> 252 33 write
#> 253 44 write
#> 254 59 write
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#> 256 39 write
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#> 258 39 write
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#> 260 49 write
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#> 262 62 write
#> 263 44 write
#> 264 33 write
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#> 273 67 write
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#> 276 40 write
#> 277 61 write
#> 278 59 write
#> 279 36 write
#> 280 41 write
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#> 283 59 write
#> 284 65 write
#> 285 41 write
#> 286 62 write
#> 287 41 write
#> 288 49 write
#> 289 31 write
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#> 293 62 write
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#> 297 65 write
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#> 299 44 write
#> 300 63 write
#> 301 60 write
#> 302 59 write
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#> 350 55 write
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#> 355 62 write
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#> 357 55 write
#> 358 57 write
#> 359 39 write
#> 360 67 write
#> 361 62 write
#> 362 50 write
#> 363 61 write
#> 364 62 write
#> 365 59 write
#> 366 44 write
#> 367 59 write
#> 368 54 write
#> 369 62 write
#> 370 60 write
#> 371 57 write
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#> 374 59 write
#> 375 49 write
#> 376 60 write
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#> 378 54 write
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#> 384 65 write
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#> 388 44 write
#> 389 62 write
#> 390 46 write
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#> 392 57 write
#> 393 52 write
#> 394 59 write
#> 395 65 write
#> 396 59 write
#> 397 46 write
#> 398 41 write
#> 399 62 write
#> 400 65 write
#> 401 41 math
#> 402 53 math
#> 403 54 math
#> 404 47 math
#> 405 57 math
#> 406 51 math
#> 407 42 math
#> 408 45 math
#> 409 54 math
#> 410 52 math
#> 411 51 math
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#> 413 71 math
#> 414 57 math
#> 415 50 math
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#> 423 45 math
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#> 428 57 math
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#> 435 50 math
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#> 437 75 math
#> 438 68 math
#> 439 44 math
#> 440 40 math
#> 441 41 math
#> 442 62 math
#> 443 57 math
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#> 445 48 math
#> 446 63 math
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#> 449 63 math
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#> 485 40 math
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#> 499 40 math
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#> 508 40 math
#> 509 46 math
#> 510 69 math
#> 511 40 math
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#> 513 57 math
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#> 517 55 math
#> 518 62 math
#> 519 64 math
#> 520 40 math
#> 521 50 math
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#> 529 56 math
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#> 552 61 math
#> 553 40 math
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#> 556 61 math
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#> 562 50 math
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#> 564 72 math
#> 565 48 math
#> 566 40 math
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#> 569 63 math
#> 570 51 math
#> 571 45 math
#> 572 39 math
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#> 574 62 math
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#> 577 63 math
#> 578 54 math
#> 579 45 math
#> 580 60 math
#> 581 49 math
#> 582 48 math
#> 583 57 math
#> 584 55 math
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#> 587 55 math
#> 588 42 math
#> 589 56 math
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#> 592 42 math
#> 593 53 math
#> 594 42 math
#> 595 60 math
#> 596 52 math
#> 597 38 math
#> 598 57 math
#> 599 58 math
#> 600 65 math
#> 601 47 science
#> 602 63 science
#> 603 58 science
#> 604 53 science
#> 605 53 science
#> 606 63 science
#> 607 53 science
#> 608 39 science
#> 609 58 science
#> 610 NA science
#> 611 53 science
#> 612 63 science
#> 613 61 science
#> 614 55 science
#> 615 31 science
#> 616 50 science
#> 617 50 science
#> 618 58 science
#> 619 NA science
#> 620 53 science
#> 621 66 science
#> 622 72 science
#> 623 55 science
#> 624 61 science
#> 625 39 science
#> 626 39 science
#> 627 61 science
#> 628 58 science
#> 629 39 science
#> 630 55 science
#> 631 47 science
#> 632 64 science
#> 633 66 science
#> 634 72 science
#> 635 61 science
#> 636 61 science
#> 637 66 science
#> 638 NA science
#> 639 36 science
#> 640 39 science
#> 641 42 science
#> 642 58 science
#> 643 55 science
#> 644 50 science
#> 645 63 science
#> 646 69 science
#> 647 49 science
#> 648 63 science
#> 649 53 science
#> 650 47 science
#> 651 57 science
#> 652 47 science
#> 653 50 science
#> 654 55 science
#> 655 69 science
#> 656 NA science
#> 657 33 science
#> 658 56 science
#> 659 58 science
#> 660 44 science
#> 661 58 science
#> 662 69 science
#> 663 34 science
#> 664 36 science
#> 665 36 science
#> 666 50 science
#> 667 55 science
#> 668 42 science
#> 669 65 science
#> 670 44 science
#> 671 39 science
#> 672 58 science
#> 673 63 science
#> 674 74 science
#> 675 58 science
#> 676 45 science
#> 677 NA science
#> 678 63 science
#> 679 39 science
#> 680 42 science
#> 681 55 science
#> 682 61 science
#> 683 66 science
#> 684 63 science
#> 685 44 science
#> 686 63 science
#> 687 53 science
#> 688 42 science
#> 689 34 science
#> 690 61 science
#> 691 47 science
#> 692 66 science
#> 693 69 science
#> 694 44 science
#> 695 47 science
#> 696 63 science
#> 697 66 science
#> 698 69 science
#> 699 39 science
#> 700 61 science
#> 701 69 science
#> 702 66 science
#> 703 33 science
#> 704 50 science
#> 705 61 science
#> 706 42 science
#> 707 50 science
#> 708 51 science
#> 709 50 science
#> 710 58 science
#> 711 61 science
#> 712 39 science
#> 713 46 science
#> 714 59 science
#> 715 55 science
#> 716 42 science
#> 717 55 science
#> 718 58 science
#> 719 58 science
#> 720 39 science
#> 721 50 science
#> 722 50 science
#> 723 39 science
#> 724 48 science
#> 725 34 science
#> 726 58 science
#> 727 44 science
#> 728 50 science
#> 729 47 science
#> 730 29 science
#> 731 50 science
#> 732 54 science
#> 733 50 science
#> 734 47 science
#> 735 44 science
#> 736 67 science
#> 737 58 science
#> 738 44 science
#> 739 42 science
#> 740 44 science
#> 741 44 science
#> 742 50 science
#> 743 39 science
#> 744 44 science
#> 745 53 science
#> 746 48 science
#> 747 55 science
#> 748 44 science
#> 749 40 science
#> 750 34 science
#> 751 42 science
#> 752 58 science
#> 753 50 science
#> 754 53 science
#> 755 58 science
#> 756 55 science
#> 757 54 science
#> 758 47 science
#> 759 42 science
#> 760 61 science
#> 761 53 science
#> 762 51 science
#> 763 63 science
#> 764 61 science
#> 765 55 science
#> 766 40 science
#> 767 61 science
#> 768 47 science
#> 769 55 science
#> 770 53 science
#> 771 50 science
#> 772 47 science
#> 773 31 science
#> 774 61 science
#> 775 35 science
#> 776 54 science
#> 777 55 science
#> 778 53 science
#> 779 58 science
#> 780 56 science
#> 781 50 science
#> 782 39 science
#> 783 63 science
#> 784 50 science
#> 785 66 science
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#> 788 42 science
#> 789 55 science
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#> 791 42 science
#> 792 50 science
#> 793 55 science
#> 794 34 science
#> 795 50 science
#> 796 42 science
#> 797 36 science
#> 798 55 science
#> 799 58 science
#> 800 53 science
#> 801 57 socst
#> 802 61 socst
#> 803 31 socst
#> 804 56 socst
#> 805 61 socst
#> 806 61 socst
#> 807 61 socst
#> 808 36 socst
#> 809 51 socst
#> 810 51 socst
#> 811 61 socst
#> 812 61 socst
#> 813 71 socst
#> 814 46 socst
#> 815 56 socst
#> 816 56 socst
#> 817 56 socst
#> 818 56 socst
#> 819 61 socst
#> 820 46 socst
#> 821 41 socst
#> 822 66 socst
#> 823 56 socst
#> 824 61 socst
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#> 826 31 socst
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#> 830 41 socst
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#> 837 66 socst
#> 838 66 socst
#> 839 36 socst
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#> 855 66 socst
#> 856 42 socst
#> 857 32 socst
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#> 864 36 socst
#> 865 61 socst
#> 866 26 socst
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#> 869 44 socst
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#> 895 51 socst
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#> 899 41 socst
#> 900 61 socst
#> 901 66 socst
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#> 906 56 socst
#> 907 56 socst
#> 908 33 socst
#> 909 56 socst
#> 910 71 socst
#> 911 56 socst
#> 912 51 socst
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#> 914 56 socst
#> 915 66 socst
#> 916 41 socst
#> 917 46 socst
#> 918 66 socst
#> 919 56 socst
#> 920 51 socst
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#> 922 56 socst
#> 923 56 socst
#> 924 46 socst
#> 925 46 socst
#> 926 61 socst
#> 927 56 socst
#> 928 41 socst
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#> 930 26 socst
#> 931 56 socst
#> 932 56 socst
#> 933 51 socst
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#> 937 46 socst
#> 938 56 socst
#> 939 41 socst
#> 940 61 socst
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#> 944 41 socst
#> 945 66 socst
#> 946 61 socst
#> 947 31 socst
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#> 949 41 socst
#> 950 41 socst
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#> 952 56 socst
#> 953 51 socst
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#> 955 66 socst
#> 956 71 socst
#> 957 61 socst
#> 958 61 socst
#> 959 41 socst
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#> 962 58 socst
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#> 965 61 socst
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#> 968 36 socst
#> 969 41 socst
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#> 971 43 socst
#> 972 61 socst
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#> 974 51 socst
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#> 976 66 socst
#> 977 71 socst
#> 978 41 socst
#> 979 36 socst
#> 980 51 socst
#> 981 51 socst
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#> 983 61 socst
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#> 985 56 socst
#> 986 71 socst
#> 987 51 socst
#> 988 36 socst
#> 989 61 socst
#> 990 66 socst
#> 991 41 socst
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#> 993 56 socst
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#> 997 46 socst
#> 998 52 socst
#> 999 61 socst
#> 1000 61 socst
read <- dta2[c(1:200), ]
write <- dta2[c(201:400), ]
math <- dta2[c(401:600), ]
science <- dta2[c(601:800), ]
socst <- dta2[c(801:1000), ]
rw <- rbind(read, write)
rw$group <- "rw"
rm <- rbind(read, math)
rm$group <- "rm"
rsc <- rbind(read, science)
rsc$group <- "rsc"
rso <- rbind(read, socst)
rso$group <- "rso"
wm <- rbind(write, math)
wm$group <- "wm"
wsc <- rbind(write, science)
wsc$group <- "wsc"
wso <- rbind(write, socst)
wso$group <- "wso"
msc <- rbind(math, science)
msc$group <- "msc"
mso <- rbind(math, socst)
mso$group <- "mso"
scso <- rbind(science, socst)
scso$group <- "scso"
dta3 <- rbind(rbind(rbind(rbind(rbind(rbind(rbind(rbind(rbind(rw, rm), rsc), rso), wm), wsc), wso), msc), mso), scso)
dta3
#> values ind group
#> 1 57 read rw
#> 2 68 read rw
#> 3 44 read rw
#> 4 63 read rw
#> 5 47 read rw
#> 6 44 read rw
#> 7 50 read rw
#> 8 34 read rw
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#> 10 57 read rw
#> 11 60 read rw
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#> 25 37 read rw
#> 26 34 read rw
#> 27 65 read rw
#> 28 47 read rw
#> 29 44 read rw
#> 30 52 read rw
#> 31 42 read rw
#> 32 76 read rw
#> 33 65 read rw
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#> 35 52 read rw
#> 36 60 read rw
#> 37 68 read rw
#> 38 65 read rw
#> 39 47 read rw
#> 40 39 read rw
#> 41 47 read rw
#> 42 55 read rw
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#> 44 42 read rw
#> 45 65 read rw
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#> 48 65 read rw
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#> 54 63 read rw
#> 55 73 read rw
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#> 70 50 read rw
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#> 79 31 read rw
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#> 93 68 read rw
#> 94 39 read rw
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#> 98 63 read rw
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#> 101 68 read rw
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#> 114 68 read rw
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#> 120 41 read rw
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#> 135 61 read rw
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#> 141 28 read rw
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#> 145 52 read rw
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#> 147 50 read rw
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#> 150 45 read rw
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#> 152 65 read rw
#> 153 43 read rw
#> 154 47 read rw
#> 155 57 read rw
#> 156 68 read rw
#> 157 52 read rw
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#> 159 42 read rw
#> 160 66 read rw
#> 161 47 read rw
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#> 195 47 read rw
#> 196 55 read rw
#> 197 42 read rw
#> 198 57 read rw
#> 199 55 read rw
#> 200 63 read rw
#> 201 52 write rw
#> 202 59 write rw
#> 203 33 write rw
#> 204 44 write rw
#> 205 52 write rw
#> 206 52 write rw
#> 207 59 write rw
#> 208 46 write rw
#> 209 57 write rw
#> 210 55 write rw
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#> 212 65 write rw
#> 213 60 write rw
#> 214 63 write rw
#> 215 57 write rw
#> 216 49 write rw
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#> 219 65 write rw
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#> 319 57 write rw
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#> 395 65 write rw
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#> 398 41 write rw
#> 399 62 write rw
#> 400 65 write rw
#> 1100 57 read rm
#> 2100 68 read rm
#> 3100 44 read rm
#> 4100 63 read rm
#> 5100 47 read rm
#> 610 44 read rm
#> 710 50 read rm
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#> 1010 57 read rm
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#> 1310 73 read rm
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#> 1910 68 read rm
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#> 601 48 read rm
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#> 621 47 read rm
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#> 671 60 read rm
#> 681 47 read rm
#> 691 63 read rm
#> 701 50 read rm
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#> 731 73 read rm
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#> 1001 63 read rm
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#> 8224 66 socst scso
#> 8233 56 socst scso
#> 8243 61 socst scso
#> 8253 46 socst scso
#> 8263 31 socst scso
#> 8273 66 socst scso
#> 8283 46 socst scso
#> 8293 46 socst scso
#> 8303 41 socst scso
#> 8314 51 socst scso
#> 8324 61 socst scso
#> 8333 71 socst scso
#> 8343 31 socst scso
#> 8353 61 socst scso
#> 8363 66 socst scso
#> 8373 66 socst scso
#> 8383 66 socst scso
#> 8393 36 socst scso
#> 8403 51 socst scso
#> 8414 51 socst scso
#> 8424 51 socst scso
#> 8433 51 socst scso
#> 8443 41 socst scso
#> 8453 66 socst scso
#> 8463 46 socst scso
#> 8473 47 socst scso
#> 8483 51 socst scso
#> 8493 46 socst scso
#> 8503 51 socst scso
#> 8514 56 socst scso
#> 8524 41 socst scso
#> 8533 46 socst scso
#> 8543 71 socst scso
#> 8553 66 socst scso
#> 8563 42 socst scso
#> 8573 32 socst scso
#> 8583 46 socst scso
#> 8593 41 socst scso
#> 8603 51 socst scso
#> 8614 61 socst scso
#> 8624 66 socst scso
#> 8633 46 socst scso
#> 8643 36 socst scso
#> 8653 61 socst scso
#> 8663 26 socst scso
#> 8673 66 socst scso
#> 8683 26 socst scso
#> 8693 44 socst scso
#> 8703 36 socst scso
#> 8714 51 socst scso
#> 8724 61 socst scso
#> 8733 66 socst scso
#> 8743 66 socst scso
#> 8753 51 socst scso
#> 8763 31 socst scso
#> 8773 61 socst scso
#> 8783 66 socst scso
#> 8793 46 socst scso
#> 8803 56 socst scso
#> 8814 56 socst scso
#> 8824 36 socst scso
#> 8833 56 socst scso
#> 8843 56 socst scso
#> 8853 41 socst scso
#> 8863 66 socst scso
#> 8873 56 socst scso
#> 8883 56 socst scso
#> 8893 31 socst scso
#> 8903 56 socst scso
#> 8914 46 socst scso
#> 8924 46 socst scso
#> 8933 61 socst scso
#> 8943 48 socst scso
#> 8953 51 socst scso
#> 8963 51 socst scso
#> 8973 56 socst scso
#> 8983 71 socst scso
#> 8993 41 socst scso
#> 9003 61 socst scso
#> 9014 66 socst scso
#> 9024 61 socst scso
#> 9033 41 socst scso
#> 9043 51 socst scso
#> 9053 51 socst scso
#> 9063 56 socst scso
#> 9073 56 socst scso
#> 9083 33 socst scso
#> 9093 56 socst scso
#> 9104 71 socst scso
#> 9114 56 socst scso
#> 9124 51 socst scso
#> 9134 66 socst scso
#> 9143 56 socst scso
#> 9153 66 socst scso
#> 9163 41 socst scso
#> 9173 46 socst scso
#> 9183 66 socst scso
#> 9193 56 socst scso
#> 9203 51 socst scso
#> 9214 51 socst scso
#> 9224 56 socst scso
#> 9233 56 socst scso
#> 9243 46 socst scso
#> 9253 46 socst scso
#> 9263 61 socst scso
#> 9273 56 socst scso
#> 9283 41 socst scso
#> 9293 46 socst scso
#> 9303 26 socst scso
#> 9314 56 socst scso
#> 9324 56 socst scso
#> 9333 51 socst scso
#> 9343 46 socst scso
#> 9353 66 socst scso
#> 9363 66 socst scso
#> 9373 46 socst scso
#> 9383 56 socst scso
#> 9393 41 socst scso
#> 9403 61 socst scso
#> 9414 51 socst scso
#> 9424 52 socst scso
#> 9433 51 socst scso
#> 9443 41 socst scso
#> 9453 66 socst scso
#> 9463 61 socst scso
#> 9473 31 socst scso
#> 9483 51 socst scso
#> 9493 41 socst scso
#> 9503 41 socst scso
#> 9514 46 socst scso
#> 9524 56 socst scso
#> 9533 51 socst scso
#> 9543 61 socst scso
#> 9553 66 socst scso
#> 9563 71 socst scso
#> 9573 61 socst scso
#> 9583 61 socst scso
#> 9593 41 socst scso
#> 9603 66 socst scso
#> 9614 61 socst scso
#> 9624 58 socst scso
#> 9633 31 socst scso
#> 9643 61 socst scso
#> 9653 61 socst scso
#> 9663 31 socst scso
#> 9673 61 socst scso
#> 9683 36 socst scso
#> 9693 41 socst scso
#> 9703 37 socst scso
#> 9714 43 socst scso
#> 9724 61 socst scso
#> 9733 39 socst scso
#> 9743 51 socst scso
#> 9753 51 socst scso
#> 9763 66 socst scso
#> 9773 71 socst scso
#> 9783 41 socst scso
#> 9793 36 socst scso
#> 9803 51 socst scso
#> 9814 51 socst scso
#> 9824 51 socst scso
#> 9833 61 socst scso
#> 9843 61 socst scso
#> 9853 56 socst scso
#> 9863 71 socst scso
#> 9873 51 socst scso
#> 9883 36 socst scso
#> 9893 61 socst scso
#> 9903 66 socst scso
#> 9914 41 socst scso
#> 9924 41 socst scso
#> 9933 56 socst scso
#> 9943 51 socst scso
#> 9953 56 socst scso
#> 9963 56 socst scso
#> 9973 46 socst scso
#> 9983 52 socst scso
#> 9993 61 socst scso
#> 10003 61 socst scso
aggregate(values ~ ind, data = dta3, FUN = mean)
#> ind values
#> 1 read 52.23000
#> 2 write 52.77500
#> 3 math 52.64500
#> 4 science 51.91795
#> 5 socst 52.40500
sapply(split(dta3, dta3$group), function(x) t.test(x$values ~ x$ind))
#> msc mso
#> statistic 0.7535309 0.2382053
#> parameter 391.0861 390.8348
#> p.value 0.4515844 0.8118467
#> conf.int Numeric,2 Numeric,2
#> estimate Numeric,2 Numeric,2
#> null.value 0 0
#> stderr 0.9648593 1.007534
#> alternative "two.sided" "two.sided"
#> method "Welch Two Sample t-test" "Welch Two Sample t-test"
#> data.name "x$values by x$ind" "x$values by x$ind"
#> rm rsc
#> statistic -0.4225787 0.3093215
#> parameter 394.804 392.8398
#> p.value 0.6728327 0.757241
#> conf.int Numeric,2 Numeric,2
#> estimate Numeric,2 Numeric,2
#> null.value 0 0
#> stderr 0.9820655 1.008825
#> alternative "two.sided" "two.sided"
#> method "Welch Two Sample t-test" "Welch Two Sample t-test"
#> data.name "x$values by x$ind" "x$values by x$ind"
#> rso rw
#> statistic -0.166712 -0.5519906
#> parameter 397.1601 395.5706
#> p.value 0.8676815 0.5812665
#> conf.int Numeric,2 Numeric,2
#> estimate Numeric,2 Numeric,2
#> null.value 0 0
#> stderr 1.049714 0.9873356
#> alternative "two.sided" "two.sided"
#> method "Welch Two Sample t-test" "Welch Two Sample t-test"
#> data.name "x$values by x$ind" "x$values by x$ind"
#> scso wm
#> statistic -0.4712025 0.1379504
#> parameter 391.2921 397.9456
#> p.value 0.6377587 0.8903494
#> conf.int Numeric,2 Numeric,2
#> estimate Numeric,2 Numeric,2
#> null.value 0 0
#> stderr 1.033635 0.9423678
#> alternative "two.sided" "two.sided"
#> method "Welch Two Sample t-test" "Welch Two Sample t-test"
#> data.name "x$values by x$ind" "x$values by x$ind"
#> wsc wso
#> statistic 0.8833551 0.3653701
#> parameter 391.6689 391.9818
#> p.value 0.3775863 0.7150322
#> conf.int Numeric,2 Numeric,2
#> estimate Numeric,2 Numeric,2
#> null.value 0 0
#> stderr 0.9702228 1.012672
#> alternative "two.sided" "two.sided"
#> method "Welch Two Sample t-test" "Welch Two Sample t-test"
#> data.name "x$values by x$ind" "x$values by x$ind"
#所有T考驗均不顯著，兩兩相較之下平均數並無差別
#(b)
dta3$race <- as.factor(dta$race)
dta3$ind <- as.factor(dta3$ind)
lapply(split(dta3, dta3$ind), function(x) anova(lm(x$values ~ factor(x$race))))
#> $read
#> Analysis of Variance Table
#>
#> Response: x$values
#> Df Sum Sq Mean Sq F value Pr(>F)
#> factor(x$race) 3 6999 2333.08 24.22 5.262e-15 ***
#> Residuals 796 76678 96.33
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> $write
#> Analysis of Variance Table
#>
#> Response: x$values
#> Df Sum Sq Mean Sq F value Pr(>F)
#> factor(x$race) 3 7657 2552.21 31.813 < 2.2e-16 ***
#> Residuals 796 63859 80.22
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> $math
#> Analysis of Variance Table
#>
#> Response: x$values
#> Df Sum Sq Mean Sq F value Pr(>F)
#> factor(x$race) 3 7369 2456.19 31.285 < 2.2e-16 ***
#> Residuals 796 62495 78.51
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> $science
#> Analysis of Variance Table
#>
#> Response: x$values
#> Df Sum Sq Mean Sq F value Pr(>F)
#> factor(x$race) 3 12678 4226.0 53.074 < 2.2e-16 ***
#> Residuals 776 61789 79.6
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> $socst
#> Analysis of Variance Table
#>
#> Response: x$values
#> Df Sum Sq Mean Sq F value Pr(>F)
#> factor(x$race) 3 3776 1258.51 11.388 2.562e-07 ***
#> Residuals 796 87969 110.51
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#這四個種族並沒有平均數相同
#(c)
rd <- dta[, "read"]
rd1 <- lapply(dta[, 8:11], function(x)lm(rd ~ x))
lapply(rd1[1:4], broom::tidy)
#> $write
#> # A tibble: 2 x 5
#> term estimate std.error statistic p.value
#> <chr> <dbl> <dbl> <dbl> <dbl>
#> 1 (Intercept) 18.2 3.31 5.49 1.21e- 7
#> 2 x 0.646 0.0617 10.5 1.11e-20
#>
#> $math
#> # A tibble: 2 x 5
#> term estimate std.error statistic p.value
#> <chr> <dbl> <dbl> <dbl> <dbl>
#> 1 (Intercept) 14.1 3.12 4.52 1.08e- 5
#> 2 x 0.725 0.0583 12.4 1.28e-26
#>
#> $science
#> # A tibble: 2 x 5
#> term estimate std.error statistic p.value
#> <chr> <dbl> <dbl> <dbl> <dbl>
#> 1 (Intercept) 18.2 3.10 5.87 1.91e- 8
#> 2 x 0.654 0.0586 11.2 1.22e-22
#>
#> $socst
#> # A tibble: 2 x 5
#> term estimate std.error statistic p.value
#> <chr> <dbl> <dbl> <dbl> <dbl>
#> 1 (Intercept) 21.1 2.84 7.43 3.22e-12
#> 2 x 0.594 0.0532 11.2 9.29e-23
we <- dta[, "write"]
we1 <- lapply(dta[, 9:11], function(x)lm(we ~ x))
lapply(we1[1:3], broom::tidy)
#> $math
#> # A tibble: 2 x 5
#> term estimate std.error statistic p.value
#> <chr> <dbl> <dbl> <dbl> <dbl>
#> 1 (Intercept) 19.9 3.02 6.58 4.20e-10
#> 2 x 0.625 0.0566 11.0 2.09e-22
#>
#> $science
#> # A tibble: 2 x 5
#> term estimate std.error statistic p.value
#> <chr> <dbl> <dbl> <dbl> <dbl>
#> 1 (Intercept) 24.4 3.03 8.03 9.27e-14
#> 2 x 0.546 0.0574 9.50 8.15e-18
#>
#> $socst
#> # A tibble: 2 x 5
#> term estimate std.error statistic p.value
#> <chr> <dbl> <dbl> <dbl> <dbl>
#> 1 (Intercept) 24.8 2.67 9.28 3.11e-17
#> 2 x 0.534 0.0500 10.7 2.45e-21
mh <- dta[, "math"]
mh1 <- lapply(dta[, 10:11], function(x)lm(mh ~ x))
lapply(mh1[1:2], broom::tidy)
#> $science
#> # A tibble: 2 x 5
#> term estimate std.error statistic p.value
#> <chr> <dbl> <dbl> <dbl> <dbl>
#> 1 (Intercept) 21.4 2.84 7.54 1.76e-12
#> 2 x 0.600 0.0537 11.2 1.06e-22
#>
#> $socst
#> # A tibble: 2 x 5
#> term estimate std.error statistic p.value
#> <chr> <dbl> <dbl> <dbl> <dbl>
#> 1 (Intercept) 27.7 2.78 9.97 3.09e-19
#> 2 x 0.475 0.0520 9.13 7.83e-17
lm(science ~ socst, dta)
#>
#> Call:
#> lm(formula = science ~ socst, data = dta)
#>
#> Coefficients:
#> (Intercept) socst
#> 30.1197 0.41672.The formula P = L (r/(1-(1+r)^(-M)) describes the payment you have to make per month for M number of months if you take out a loan of L amount today at a monthly interest rate of r.
Compute how much you will have to pay per month for 10, 15, 20, 25, or 30 years if you borrow NT$5,000,000, 10,000,000, or 15,000,000 from a bank that charges you 2%, 5%, or 7% for the monthly interest rate.
dta <- function(L, r, M) {print(L*(r/(1-(1+r)^(-M))))}
dta(5000000, 0.02, c(10, 15, 20, 25, 30))
#> [1] 556632.6 389127.4 305783.6 256102.2 223249.6
dta(10000000, 0.05, c(10, 15, 20, 25, 30))
#> [1] 1295045.7 963422.9 802425.9 709524.6 650514.4
dta(15000000, 0.02, c(10, 15, 20, 25, 30))
#> [1] 1669897.9 1167382.1 917350.8 768306.6 669748.83.The following R script is an attempt to demonstrate the correspondence between parameter estimations by the least square method and the maximum likelihood method for the case of simple linear regression with a constant normal error term.
1.Construct a function from the script so that any deviance value for pairs of parameter estimates can be found.
2.Generalize the function further so that it will work with any data sets that can be modeled by a simple linear regression with a constant normal error term.
##
m0 <- lm(weight ~ height, data=women)
##
summary(m0)
#>
#> Call:
#> lm(formula = weight ~ height, data = women)
#>
#> Residuals:
#> Min 1Q Median 3Q Max
#> -1.7333 -1.1333 -0.3833 0.7417 3.1167
#>
#> Coefficients:
#> Estimate Std. Error t value Pr(>|t|)
#> (Intercept) -87.51667 5.93694 -14.74 1.71e-09 ***
#> height 3.45000 0.09114 37.85 1.09e-14 ***
#> ---
#> Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
#>
#> Residual standard error: 1.525 on 13 degrees of freedom
#> Multiple R-squared: 0.991, Adjusted R-squared: 0.9903
#> F-statistic: 1433 on 1 and 13 DF, p-value: 1.091e-14
##
param <- c(coef(m0)[1], coef(m0)[2])
##
a <- param[1]
##
b <- param[2]
##
yhat <- a + b*women$height
##
e <- summary(m0)$sigma
##
lkhd <- dnorm(women$weight, mean=yhat, sd=e)
##
dvnc <- -2 * sum(log(lkhd))
##
ci_a <- coef(m0)[1] + unlist(summary(m0))$coefficients3*c(-2,2)
##
ci_b <- coef(m0)[2] + unlist(summary(m0))$coefficients4*c(-2,2)
##
bb <- expand.grid(a=seq(ci_a[1], ci_a[2], len=50),
b=seq(ci_b[1], ci_b[2], len=50))
## Not working yet
#bb$d <- apply(bb, 1, dvnc_fun)
#didn't finish
##4.Modify this R script to create a function to compute the c-statistic illustrated with the data set in the article: Tryon, W.W. (1984). A simplified time-series analysis for evaluating treatment interventions. Journal of Applied Behavioral Analysis, 34(4), 230-233.
#
# c-stat example
#
# read in data
dta <- read.table("C:/Users/boss/Desktop/data_management/cstat.txt", header=T)
str(dta)
#> 'data.frame': 42 obs. of 1 variable:
#> $ nc: int 28 46 39 45 24 20 35 37 36 40 ...
head(dta)
#> nc
#> 1 28
#> 2 46
#> 3 39
#> 4 45
#> 5 24
#> 6 20
dim(dta)
#> [1] 42 1
#
# plot figure 1
#
plot(1:42, dta[,1], xlab="Observations", ylab="Number of Children")
lines(1:42, dta[,1])
abline(v=10, lty=2)
abline(v=32, lty=2)
segments(1, mean(dta[1:10,1]),10, mean(dta[1:10,1]),col="red")
segments(11, mean(dta[11:32,1]),32, mean(dta[11:32,1]),col="red")
segments(33, mean(dta[33:42,1]),42, mean(dta[33:42,1]),col="red")
#
# calculate c-stat for first baseline phase
#
cden <- 1-(sum(diff(dta[1:10,1])^2)/(2*(10-1)*var(dta[1:10,1])))
sc <- sqrt((10-2)/((10-1)*(10+1)))
pval <- 1-pnorm(cden/sc)
pval
#> [1] 0.2866238
#
# calculate c-stat for first baseline plus group tokens
#
n <- 32
cden <- 1-(sum(diff(dta[1:n,1])^2)/(2*(n-1)*var(dta[1:n,1])))
sc <- sqrt((n-2)/((n-1)*(n+1)))
pval <- 1-pnorm(cden/sc)
list(z=cden/sc,pvalue=pval)
#> $z
#> [1] 3.879054
#>
#> $pvalue
#> [1] 5.243167e-05
###
#didn't finish5.Plot the likelihood function to estimate the probability of graduate admission by gender, respectively, for Dept A in UCBAdmissions{datasets}. Construct approximate 95%-CI for each gender. Do they overlap?
dta <- datasets::UCBAdmissions
dta
#> , , Dept = A
#>
#> Gender
#> Admit Male Female
#> Admitted 512 89
#> Rejected 313 19
#>
#> , , Dept = B
#>
#> Gender
#> Admit Male Female
#> Admitted 353 17
#> Rejected 207 8
#>
#> , , Dept = C
#>
#> Gender
#> Admit Male Female
#> Admitted 120 202
#> Rejected 205 391
#>
#> , , Dept = D
#>
#> Gender
#> Admit Male Female
#> Admitted 138 131
#> Rejected 279 244
#>
#> , , Dept = E
#>
#> Gender
#> Admit Male Female
#> Admitted 53 94
#> Rejected 138 299
#>
#> , , Dept = F
#>
#> Gender
#> Admit Male Female
#> Admitted 22 24
#> Rejected 351 317
dta1 <- as.data.frame(dta)
dta1
#> Admit Gender Dept Freq
#> 1 Admitted Male A 512
#> 2 Rejected Male A 313
#> 3 Admitted Female A 89
#> 4 Rejected Female A 19
#> 5 Admitted Male B 353
#> 6 Rejected Male B 207
#> 7 Admitted Female B 17
#> 8 Rejected Female B 8
#> 9 Admitted Male C 120
#> 10 Rejected Male C 205
#> 11 Admitted Female C 202
#> 12 Rejected Female C 391
#> 13 Admitted Male D 138
#> 14 Rejected Male D 279
#> 15 Admitted Female D 131
#> 16 Rejected Female D 244
#> 17 Admitted Male E 53
#> 18 Rejected Male E 138
#> 19 Admitted Female E 94
#> 20 Rejected Female E 299
#> 21 Admitted Male F 22
#> 22 Rejected Male F 351
#> 23 Admitted Female F 24
#> 24 Rejected Female F 317
dta2 <- subset(dta1, dta1$Dept == "A")
dta2
#> Admit Gender Dept Freq
#> 1 Admitted Male A 512
#> 2 Rejected Male A 313
#> 3 Admitted Female A 89
#> 4 Rejected Female A 19
set.seed(1993)
n <- 100000
p_male <- 512/825
p_female <- 89/118
y_male <- rbinom(n, 1, p_male)
y_female <- rbinom(n, 1, p_female)
theta <- seq(0.01, 0.99, by=.01)
lklhd_male <- sum(y_male) * log(theta) + (n - sum(y_male)) * log(1 - theta)
lklhd_female <- sum(y_female) * log(theta) + (n - sum(y_female)) * log(1 - theta)
plot(theta, lklhd_female, xlab = 'Probability', ylab = 'Likelihood', main = 'Grid search', type='n')
lines(theta, lklhd_male, col = 'blue')
phat_male <- mean(y_male)
abline(v = phat_male, lty = 3, col = 'blue')
arrows(phat_male - 2*sqrt(phat_male*(1-phat_male))/sqrt(n),
-1000,
phat_male + 2*sqrt(phat_male*(1-phat_male))/sqrt(n),
-1000,
code=3,
length=0.1, angle=90)
lines(theta, lklhd_female, col = 'pink')
phat_female <- mean(y_female)
abline(v = phat_female, lty = 3, col = 'pink')
arrows(phat_female - 2*sqrt(phat_female*(1-phat_female))/sqrt(n),
-1000,
phat_female + 2*sqrt(phat_female*(1-phat_female))/sqrt(n),
-1000,
code=3,
length=0.1, angle=90)
legend("topleft", legend = c('Male', 'Female'), cex = 1, lty = 1,
col = c('blue', 'pink'), bty = 'n')
grid()
6.(Bonus) The data set contains inter-response times (in milliseconds) in the resting activity of a single neuron recorded from the spinal cord of a cat. Write a function to fit an exponential distribution to the data. More specifically, estimate the rate parameter of the exponential distribution using the maximum likelihood method. Source: McGill, W.J. (1963). Luce, Bush, & Galanter, eds. Handbook of Mathematical Psychology.