W4

install.packages("https://cran.rstudio.com/bin/windows/contrib/4.1/faraway_1.0.7.zip", repos = NULL)

## 將程式套件安載入 'C:/Users/user/Documents/R/win-library/4.1'
## (因為 'lib' 沒有被指定)

## package 'faraway' successfully unpacked and MD5 sums checked

library("faraway")

## Warning: 套件 'faraway' 是用 R 版本 4.1.2 來建造的

install.packages("https://cran.rstudio.com/bin/windows/contrib/4.1/moments_0.14.zip", repos= NULL)

## 將程式套件安載入 'C:/Users/user/Documents/R/win-library/4.1'
## (因為 'lib' 沒有被指定)

## package 'moments' successfully unpacked and MD5 sums checked

library("moments")

## Warning: 套件 'moments' 是用 R 版本 4.1.1 來建造的

data("hsb")

#顯示前6筆
head(hsb)

##    id gender  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

#資料結構
str(hsb)

## 'data.frame':    200 obs. of  11 variables:
##  $ id     : int  70 121 86 141 172 113 50 11 84 48 ...
##  $ gender : Factor w/ 2 levels "female","male": 2 1 2 2 2 2 2 2 2 2 ...
##  $ race   : Factor w/ 4 levels "african-amer",..: 4 4 4 4 4 4 1 3 4 1 ...
##  $ ses    : Factor w/ 3 levels "high","low","middle": 2 3 1 1 3 3 3 3 3 3 ...
##  $ schtyp : Factor w/ 2 levels "private","public": 2 2 2 2 2 2 2 2 2 2 ...
##  $ prog   : Factor w/ 3 levels "academic","general",..: 2 3 2 3 1 1 2 1 2 1 ...
##  $ 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 50 ...
##  $ socst  : int  57 61 31 56 61 61 61 36 51 51 ...

#資料摘要
summary(hsb)

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

計算不同性別的平均數

with(hsb, aggregate(hsb[, 7:11], by = list(gender), FUN = mean))

##   Group.1     read    write     math  science    socst
## 1  female 51.73394 54.99083 52.39450 50.69725 52.91743
## 2    male 52.82418 50.12088 52.94505 53.23077 51.79121

計算不同性別的標準差

with(hsb, aggregate(hsb[, 7:11], by = list(gender), FUN = sd))

##   Group.1     read     write     math   science    socst
## 1  female 10.05783  8.133715 9.151015  9.038503 10.23441
## 2    male 10.50671 10.305161 9.664784 10.732171 11.33384

計算不同性別的偏態

with(hsb, aggregate(hsb[, 7:11], by = list(gender), FUN = skewness))

##   Group.1       read      write      math   science      socst
## 1  female 0.32341745 -0.5899993 0.2346739 -0.130718 -0.3532812
## 2    male 0.04674873 -0.1798980 0.3256960 -0.345221 -0.3713532

計算不同性別的峰度

with(hsb, aggregate(hsb[, 7:11], by = list(gender), FUN = kurtosis))

##   Group.1     read    write     math  science    socst
## 1  female 2.500028 2.544105 2.284784 2.510875 2.519207
## 2    male 2.262737 1.872877 2.356806 2.371868 2.335229

計算不同族群的平均數

with(hsb, aggregate(hsb[, 7:11], by = list(race), FUN = mean))

##        Group.1     read    write     math  science    socst
## 1 african-amer 46.80000 48.20000 46.75000 42.80000 49.45000
## 2        asian 51.90909 58.00000 57.27273 51.45455 51.00000
## 3     hispanic 46.66667 46.45833 47.41667 45.37500 47.79167
## 4        white 53.92414 54.05517 53.97241 54.20000 53.68276

計算不同族群的標準差

with(hsb, aggregate(hsb[, 7:11], by = list(race), FUN = sd))

##        Group.1      read    write      math  science     socst
## 1 african-amer  7.120024 9.322299  6.487843 9.445690 10.850540
## 2        asian  7.660999 7.899367 10.120187 9.490665  9.746794
## 3     hispanic 10.239169 8.272422  6.983936 8.218815  9.250049
## 4        white 10.276783 9.172558  9.383011 9.094870 10.813253

計算不同族群的偏態

with(hsb, aggregate(hsb[, 7:11], by = list(race), FUN = skewness))

##        Group.1        read      write       math    science      socst
## 1 african-amer  0.56341685  0.2445555  1.5769616  0.1618054 -0.3779222
## 2        asian -0.14903573 -0.8732263 -0.2921502 -0.3239360  0.3398069
## 3     hispanic  0.64286691  0.3420989  0.1538455  0.2121507  0.1741367
## 4        white  0.05686143 -0.7452076  0.1120681 -0.2394562 -0.5568882

計算不同族群的峰度

with(hsb, aggregate(hsb[, 7:11], by = list(race), FUN = kurtosis))

##        Group.1     read    write     math  science    socst
## 1 african-amer 4.394131 2.069851 5.739716 1.833490 2.553280
## 2        asian 2.457166 2.518799 1.843283 2.240411 2.849030
## 3     hispanic 3.381917 2.777992 2.494265 3.361737 2.218556
## 4        white 2.203770 2.710911 2.351510 2.506333 2.641000