第2章のRコード

第2章 統計の基礎知識

乱数の設定

set.seed(2022)

2.1 母集団と標本

rnorm(100, 50, 10)
  [1] 59.00142 38.26654 41.02515 35.55499 46.68986 20.99371 39.40744 52.77955
  [9] 57.49486 52.41583 60.06186 48.14854 40.18173 50.92908 49.47216 49.19672
 [17] 43.45896 40.49316 60.19562 58.59046 53.64461 53.83651 61.13406 62.11510
 [25] 46.51675 41.40447 56.50027 53.28059 44.82053 47.61018 51.17779 58.31518
 [33] 34.41081 47.79481 41.82806 60.76677 60.79664 51.42128 51.56980 48.31280
 [41] 47.30962 58.07768 38.75283 35.69212 50.60357 42.07018 53.40276 47.40531
 [49] 36.95151 53.68173 66.93190 59.95837 51.86752 62.38337 53.09373 56.35718
 [57] 50.23183 61.77864 45.46453 54.15928 36.61558 37.08025 46.90926 51.56512
 [65] 41.66083 49.75451 38.62648 60.72054 73.14499 54.22973 48.63061 63.28397
 [73] 54.36536 50.66429 63.04660 47.90740 60.18253 63.66035 64.76696 58.87307
 [81] 39.84091 68.70869 60.76198 39.25592 28.04424 55.34545 63.43733 63.85004
 [89] 77.46927 49.54055 57.43085 52.60425 54.28282 46.31741 78.87423 43.92927
 [97] 31.20801 57.18357 52.51426 54.67023
curve(dnorm(x, 50, 10), 0, 100, xlab = "", ylab = "")

pnorm(60, 50, 10)
[1] 0.8413447

2.2 無作為抽出

rnorm(100, 50, 10)
  [1] 47.82112 37.82352 42.45921 51.91230 60.47283 60.89828 56.95474 44.75631
  [9] 52.64016 62.41200 56.43297 40.03237 29.97702 45.24161 50.44180 36.18865
 [17] 52.47520 52.24190 58.61479 40.73238 46.79557 56.73025 37.34370 44.81479
 [25] 61.22494 46.84022 32.41701 62.37253 33.36048 68.55734 60.57997 50.37269
 [33] 50.04605 30.56166 34.30377 47.26703 54.68854 60.32539 35.81604 49.12122
 [41] 65.78631 52.44625 64.97093 59.15906 53.20841 55.62724 55.39295 39.26595
 [49] 31.16839 59.11390 50.49596 37.64345 37.36248 38.57135 56.54412 43.23181
 [57] 39.26090 40.24342 38.73725 30.30687 44.18011 32.37493 44.72174 36.25672
 [65] 30.66287 59.79783 35.04310 67.00810 35.98974 45.15537 37.83821 51.04771
 [73] 47.57463 35.84219 39.50540 52.69057 45.21284 47.00552 60.38149 60.28925
 [81] 30.28325 37.16670 50.48581 62.10631 45.15329 42.06690 51.72414 61.05213
 [89] 57.40876 47.58553 56.14957 63.82546 44.16797 48.02070 43.96771 39.11352
 [97] 51.83915 63.07136 48.31717 53.43841
Z <- rnorm(100, 50, 10)

Z
  [1] 53.76475 48.05460 28.84664 40.86933 53.49709 54.05577 55.05326 32.08133
  [9] 43.38511 46.27727 51.58661 43.21588 50.82489 62.43740 58.80496 55.43959
 [17] 42.09095 54.27145 59.51114 58.20117 31.89054 47.20086 56.71068 65.96973
 [25] 42.74268 59.60575 59.56440 62.65848 47.63044 34.79886 53.39553 63.95974
 [33] 38.13938 45.95528 47.12894 59.42586 39.45261 43.42722 45.85711 54.53967
 [41] 44.46046 53.53869 51.48286 53.76512 65.06987 40.72705 44.12859 74.58926
 [49] 56.73742 53.34424 66.09042 38.84601 50.10130 39.47642 54.33923 56.58090
 [57] 35.59927 54.73361 41.94148 42.14534 38.64649 40.88575 50.89966 47.63905
 [65] 66.27579 55.05201 50.37437 53.65165 36.05399 56.35135 45.22247 41.80026
 [73] 62.52384 36.81650 55.44261 48.13103 56.15964 55.27988 52.34455 48.87702
 [81] 36.83703 46.63232 54.78410 39.06088 62.61406 50.36015 68.81067 41.33545
 [89] 40.05152 34.82766 49.59823 32.13462 59.56246 47.19504 45.88813 45.36570
 [97] 25.45063 53.12886 42.08662 52.25465
hist(Z)

Z[1:10]
 [1] 53.76475 48.05460 28.84664 40.86933 53.49709 54.05577 55.05326 32.08133
 [9] 43.38511 46.27727
a <- c(5, 10, 100)
Z[a]
[1] 53.49709 46.27727 52.25465
Z[c(5, 10, 100)]
[1] 53.49709 46.27727 52.25465
max(Z)
[1] 74.58926
which.max(Z)
[1] 48
min(Z)
[1] 25.45063
which.min(Z)
[1] 97
mean(Z)
[1] 49.36427
summary(Z)
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  25.45   42.09   50.23   49.36   55.32   74.59 
1:10
 [1]  1  2  3  4  5  6  7  8  9 10
sample(1:10, 3)
[1] 8 9 4
sample(Z, 5)
[1] 38.64649 44.46046 62.43740 39.47642 45.85711
fruits <- c("ミカン", "バナナ", "リンゴ", "レモン", "モモ")
よくある間違い 
fruits <- c(ミカン, バナナ, リンゴ, レモン, モモ)
Error: object 'ミカン' not found
sample(fruits,  1)
[1] "リンゴ"
sample(fruits, 2)
[1] "バナナ" "ミカン"
coin <- c("Head",  "Tail")

sample(coin, 5, replace = TRUE) # わかりづらい例なので再試行
[1] "Tail" "Tail" "Tail" "Tail" "Tail"
sample(coin, 5, replace = TRUE) # こちらの結果を掲載
[1] "Tail" "Tail" "Tail" "Head" "Head"

2.3 平均と大数の法則

mean(rnorm(100, 50, 10))
[1] 49.95459
S <- 1000
rec <- numeric(S)
for(i in 1:S){
  
  rec[i] <- mean(rnorm(100, 50, 10))
  
}
numeric(10)
 [1] 0 0 0 0 0 0 0 0 0 0
summary(rec)
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  46.61   49.31   49.98   49.98   50.62   52.70 
for(i in 1:S){
  
  rec[i] <- mean(rnorm(10000, 50, 10))
  
}

summary(rec)
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  49.66   49.93   50.00   50.00   50.07   50.32 
mean(sample(1:6, 10, replace = TRUE))
[1] 4.1
S <- 1000
rec <- numeric(S)

for(i in 1:S){
  
  rec[i] <- mean(sample(1:6, 10, replace = TRUE))
  
}

summary(rec)
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
   1.60    3.10    3.50    3.51    3.90    5.20 
S <- 1000
rec <- numeric(S)

for(i in 1:S){
  
  rec[i] <- mean(sample(1:6, 1000, replace = TRUE))
  
}

summary(rec)
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  3.336   3.460   3.498   3.496   3.533   3.673 
S <- 1000
rec <- numeric(S)

for(i in 1:S){
  
  rec[i] <- mean(sample(1:6, 10000, replace = TRUE))
  
}

summary(rec)
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  3.437   3.487   3.500   3.500   3.513   3.554

2.4 分散と標準偏差

x <- rnorm(1000, 50, 10)

var(x)
[1] 101.8111
sd(x)
[1] 10.09015
S <- 1000; n <- 1000
rec <- numeric(S)

for(i in 1:S){
  
  rec[i] <- sd(rnorm(n, 50, 10))
}

summary(rec)
   Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
  9.150   9.848  10.005  10.002  10.163  10.874

2.5 相関係数と共分散

set.seed(2022) # 乱数の再設定

x <- rnorm(100, 50, 10)
y <- rnorm(100, 50, 10)

plot(x, y)

z <- (x + y) / 2

plot(x, z)

cor(x, y)
[1] 0.05702949
cor(x, z)
[1] 0.7279044
cov(x, y)
[1] 5.917713