Kenji Saito
January 25, 2024
36

# R を用いた分析(補講) (2) — 人工データの生成 / Generating Artificial Data

January 25, 2024

## Transcript

1. ### generated by Stable Diffusion XL v1.0 2023 12 R (

) (2) — (WBS) 2023 12 R ( ) (2) — — 2024-01 – p.1/14

– p.2/14
3. ### ( 20 ) 1 • 2 R • 3 •

4 • 5 • 6 ( ) • 7 (1) • 8 (2) • 9 R ( ) (1) — Welch • 10 R ( ) (2) — χ2 • 11 R ( ) (1) — • 12 R ( ) (2) — • 13 GPT-4 14 GPT-4 15 ( ) LaTeX Overleaf 8 (12/21 ) / (2 ) OK / 2023 12 R ( ) (2) — — 2024-01 – p.3/14
4. ### N(µ, σ2) ρ 2 ( : ˆ y = a

+ b1 x1 + b2 x2 + e ) 2023 12 R ( ) (2) — — 2024-01 – p.4/14
5. ### N(µ, σ2) “rnorm()” set.seed(173205) # # N(50, 10^2) 100 x

<- rnorm(n=100, mean=50, sd=10) # x # hist(x) mean(x) sd(x) 2023 12 R ( ) (2) — — 2024-01 – p.5/14
6. ### Histogram of x x Frequency 10 20 30 40 50

60 70 80 0 5 10 15 20 25 30 35 mean(x) : 50.06994 sd(x) : 10.30096 2023 12 R ( ) (2) — — 2024-01 – p.6/14
7. ### ρ 2 (1/2) MASS “mvrnorm()” “ .R” # r =

0.9 # t = 3.7 # r = 15.2 # t = 7.5 # = -0.5 # <- matrix(c( r^2, * t * r, * r * t, t^2 ), nrow=2) 2023 12 R ( ) (2) — — 2024-01 – p.7/14
8. ### “mvrnorm()” = S xx S xy S xy S yy

= S xx rS x S y rS x S y S yy ( r = S xy S x S y ) 2 x, y x, y, z, . . . 2023 12 R ( ) (2) — — 2024-01 – p.8/14
9. ### ρ 2 (2/2) MASS “mvrnorm()” “ .R” # set.seed(28284) <-

mvrnorm(n=100, mu=c( r, t), Sigma= ) <- pmin(pmax( [,1], 13.0), 19.9) <- pmin(pmax( [,2], 0.0), 20.0) “ [,1]” “ [,2]” plot 2023 12 R ( ) (2) — — 2024-01 – p.9/14
10. ### 0 5 10 15 20 13 14 15 16 17

18 ㈇ࡢ┦㛵ࡢ౛ 㐌ᙜࡓࡾࡢㄢእ㐠ື᫬㛫 100m㉮ࡢࢱ࢖࣒ (⛊) r : -0.5932345 ( ) -0.5884094 ( ) 2023 12 R ( ) (2) — — 2024-01 – p.10/14
11. ### (1/2) “ .R” n <- 50 # a <- 49.4

# ( (158cm ) ) # r_father <- 0.306 mean_father <- 168.78 sd_father <- 3.2 # r_mother <- 0.37 mean_mother <- 155.32 sd_mother <- 2.45 2023 12 R ( ) (2) — — 2024-01 – p.11/14
12. ### (2/2) “ .R” <- round(rnorm(n=n, mean=mean_father, sd=sd_father), digits=1) <- round(rnorm(n=n,

mean=mean_mother, sd=sd_mother), digits=1) e <- rnorm(n=n, mean=0, sd=2.8) # <- round(a + r_father * + r_mother * + e, digits=1) 1 “round()” plot 2023 12 R ( ) (2) — — 2024-01 – p.12/14
13. ### ፉ㌟㛗 160 165 170 175 152 156 160 164 160

165 170 175 ∗㌟㛗 152 156 160 164 150 154 158 150 154 158 ẕ㌟㛗 : 34.2484 : 0.3545 : 0.4137 : 0.2831 2023 12 R ( ) (2) — — 2024-01 – p.13/14

p.14/14