inclass_w8

Q1

dta <- read.table("hs0.txt", h = T)

dta.asian <- subset(dta, race=="asian") #只抽亞洲人
r0 <- cor(dta.asian$math, dta.asian$socst) 

nIter <- 1001
#使用function
cnt <- function(nIter = 1001){
    new <- replicate(nIter, sample(dta.asian$read))
    r <- cor(new, dta.asian$math)
    sum( r0 <= r )
    }
cnt()/nIter

[1] 0.04195804

#使用while
i = 1
cnt = 0
while(i <= nIter){
  new <- sample(dta.asian$read)
  r <- cor(new,dta.asian$math)
  if(r0 <= r) cnt <- cnt+1
  i = i+1
}
cnt/nIter

[1] 0.04195804

Q2

#做布朗運動，隨機抽樣x,y，下一個運動點累加。
Brownian <- function(n = 11, pause = 0.05, nIter = 2, ...) {
  x = rnorm(n)
  y = rnorm(n)
  for (i in 1:nIter) {
    plot(x, y, ...)
    text(x, y, cex = 0.5)
    x = x + rnorm(n)
    y = y + rnorm(n)
    Sys.sleep(pause)
  }
} 

## test it
Brownian(xlim = c(-20, 20), ylim = c(-20, 20), 
         pch = 21, cex = 2, col = "cyan", bg = "lavender") 

###

Q3

# draw n 
newHeight <- function(n){
  set.seed(7)
  gender <- sample(c("M", "F"), n, replace = T, prob = c(0.505,0.495))
  height <- ifelse(gender == "F",
                    rnorm(n, 160,5),
                    rnorm(n, 170,7))
  data.frame(gender, height)
}
newHeight(10)

   gender   height
1       F 155.2636
2       M 163.7434
3       M 167.8487
4       M 169.9662
5       M 176.9171
6       F 161.7849
7       M 174.9374
8       F 171.4073
9       M 160.2840
10      M 178.9104