Inclass0416

Ex1

#讀取資料
dta <- read.table("hs0.txt", header = T)
#只看race為asian的資料
dta.asian <- subset(dta, race=="asian")
#看math與socst的相關係數
r0 <- cor(dta.asian$math, dta.asian$socst)
#參數設定
cnt <- 0
nIter <- 1001

#將read資料隨機排列後，與math求相關係數，重複1001次
#並記錄read與math的相關係數大於等於math與socst的相關係數的次數
#最後算出比例
for (i in 1:nIter) {
  new <- sample(dta.asian$read)
  r <- cor(new, dta.asian$math)
  if ( r0 <= r ) cnt <- cnt+1
}
cnt/nIter

## [1] 0.03796204

不使用for迴圈的寫法

dta <- read.table("hs0.txt", header = T)
dta.asian <- subset(dta, race=="asian")
r0 <- cor(dta.asian$math, dta.asian$socst)
cnt <- 0
nIter <- 1001
i <- 1

repeat{
  new <- sample(dta.asian$read)
  r <- cor(new, dta.asian$math)
  i=i+1
  if ( r0 <= r ) cnt <- cnt+1
  if (i>=nIter) break}
cnt/nIter

## [1] 0.05594406

Ex2

跑出一樣本數為n的布朗運動圖nIter張

Brownian <- function(n = 20, pause = 0.05, nIter = 3, ...) {
  x = rnorm(n)
  y = rnorm(n)
  i = 1
  while (i <= nIter) {
    plot(x, y, ...)
    text(x, y, cex = 0.5)
    x = x + rnorm(n)
    y = y + rnorm(n)
    Sys.sleep(pause)
    i = i + 1
  }
} 
### test it
Brownian(xlim = c(-20, 20), ylim = c(-20, 20), 
         pch = 21, cex = 2, col = "cyan", bg = "lavender") 

不使用for迴圈的寫法

Brownian <- function(n = 20, pause = 0.05, nIter = 3, ...) {
    x = rnorm(n)
    y = rnorm(n)
    i = 1
    repeat {
      plot(x, y, ...)
      text(x, y, cex = 0.5)
      x = x + rnorm(n)
      y = y + rnorm(n)
      Sys.sleep(pause)
      i = i + 1
      if(i >= nIter) break
    }
} 
Brownian(xlim = c(-20, 20), ylim = c(-20, 20), 
    pch = 21, cex = 2, col = "cyan", bg = "lavender") 

Ex3

隨機產生一個n*2的矩陣資料，第一行為性別(男女)，第二行為身高(公分)

出現男生機率為0.505，出現女生機率為0.495

男生身高平均數為170標準差為7

女生身高平均數為160標準差為5

simSexHeight <- function(n)  {
   m <- matrix(nrow=n, ncol=2)
   m[, 1] <- runif(n)
   m[, 2] <- rnorm(n)
   draw <- function(mr) {  # mr = one row of m
      if (mr[1] < 0.505) {
         sex <- 1
         cm <- 170 + 7*mr[2]
      } else {
         sex <- 0
         cm <- 160 + 5*mr[2] 
      }
      return(c(sex, cm))
   }
   person <- t(apply(m, 1, draw))
   person <- as.data.frame(person)
   person[, 1] <- ifelse(person[, 1]==1, "M", "F")
   names(person) <- c("Gender", "Height")
   return(person)
}
simSexHeight(5)

##   Gender   Height
## 1      M 177.9718
## 2      F 163.7873
## 3      F 161.1460
## 4      M 176.4151
## 5      M 174.7751

improve

NEW_simSexHeight <- function(n){
  m <- matrix(nrow=n, ncol=2)
   m[, 1] <- runif(n)
   m[, 2] <- rnorm(n)
   Gender <- ifelse(m[, 1] < 0.505, "M", "F")
   Height <- ifelse(m[, 1] < 0.505, 170 + 7*m[, 2],160 + 5*m[, 2])
   Person <- data.frame(Gender,Height)
return(Person)
}

NEW_simSexHeight(5)

##   Gender   Height
## 1      M 181.1997
## 2      F 170.4683
## 3      F 157.4666
## 4      M 173.2316
## 5      M 174.9778