20151208Demo.Rmd

---
title: "20151208Demo"
author: "David Chiu"
date: "2015年12月8日"
output: html_document
---

```
hist(rnorm(1000,mean=70, sd=30))

sample(1:10)
sample(1:10, size = 5)
sample(1:42, size = 6)
sample(c(0,1), 2)
sample(c(0,1), 3)

sample(c(0,1), 10, replace = TRUE)
sample.int(20, 12)

```


```
coins = c("heads", "tails")
fair_coin = sample(coins, size = 100, replace = TRUE)
table(fair_coin)

dice = sample(1:6, size=1000,replace=TRUE)
table(dice)
barplot(table(dice))


outcomes = c("head", "tail")
unfair_coin = sample(outcomes, size = 100, replace = TRUE, prob = c(0.3,0.7))
table(unfair_coin)

```

```
rnorm(100)
hist(rnorm(100))

set.seed(123)
sample(1:10, 3)

set.seed(123)
sample(1:42, 6)
sample(1:42, 6)

set.seed(123)
head(.Random.seed)

set.seed(50)
head(.Random.seed)




```


```
names(ames)
str(ames)

area = ames$Gr.Liv.Area
hist(area)
shapiro.test(area)


sample_means10 = rep(NA, 5)
rep(NA, 5)

a = c()
for(i in 1:3){
 a = c(a, i)
}


a = rep(NA,3)
for(i in 1:3){
 a[i] = i
}


sample_means10 = rep(NA, 5000)
sample_means50 = rep(NA, 5000)
sample_means100 = rep(NA, 5000)
sample(area, 10)

for (i in 1:5000){
  sample_means10[i] = mean(sample(area, 10))
}

hist(sample_means10)

for (i in 1:5000){
  sample_means50[i] = mean(sample(area, 50))
}

hist(sample_means50)


for (i in 1:5000){
  sample_means100[i] = mean(sample(area, 100))
}

hist(sample_means100)

par(mfrow = c(3, 1))

xlimits = range(sample_means10)

hist(sample_means10, breaks = 20, xlim = xlimits)
hist(sample_means50, breaks = 20, xlim = xlimits)
hist(sample_means100, breaks = 20, xlim = xlimits)


```


```

curve(dnorm, -3,3)
pnorm(1) - pnorm(-1)
x = c(-1.96,seq(-1.96,1.96,0.1),1.96)
y = c(0,dnorm(seq(-1.96,1.96,0.1)),0)
polygon(x,y, col = "red")


a = rnorm(1000)
shapiro.test(a)
b = rpois(1000, lambda = 3)
hist(b)
shapiro.test(b)

```

```
population = ames$Gr.Liv.Area
mean(population)

samp = sample(population, 50)
sample_mean = mean(samp)
hist(samp)

sde = sd(samp)/sqrt(50)

lower = sample_mean - 1.96 * sde
upper = sample_mean + 1.96 * sde

dens <- density(population)
plot(dens, col="red")
mean(population)
abline(v = mean(population), col="blue")

lower
upper
polygon(c(lower, dens$x[dens$x>lower & dens$x < upper], upper), c(0, dens$y[dens$x>=lower & dens$x <= upper], 0), col="red", density = c(10, 50) ,angle = c(-45, 45))


curve(dnorm, -3,3)
x = c(-1.96,seq(-1.96,1.96,0.1),1.96)
y = c(0,dnorm(seq(-1.96,1.96,0.1)),0)
polygon(x,y, col = "red")

alpha = 0.05
1 - alpha / 2
qnorm(1 - alpha / 2)
qnorm( 1 - (1 - alpha / 2))

alpha = 0.01
1 - alpha / 2
qnorm(1 - alpha / 2)
qnorm( 1 - (1 - alpha / 2))


lower = sample_mean - 2.58 * sde
upper = sample_mean + 2.58 * sde

polygon(c(lower, dens$x[dens$x>lower & dens$x < upper], upper), c(0, dens$y[dens$x>=lower & dens$x <= upper], 0), col="green", density = c(10, 50) ,angle = c(-45, 45))

```


```
x = c(160,170,180)
y = c(64, 68, 72)

cov_xy = sum((x - mean(x)) * (y - mean(y))) / 2
cov(x,y)

cor_xy = (sum((x - mean(x)) * (y - mean(y))) / 2) / (sd(x) * sd(y))  
cor(x,y)

plot(x,y)


data(mtcars)
mtcars

cov(mtcars)
cor(mtcars)
cov(mtcars[1:3])


gdp = read.csv("gdp.csv",header=TRUE)

gdp = gdp[1:15,]
gdp$GDP = as.numeric(sub(",", "", gdp$GDP))
gdp$Export = as.numeric(sub(",", "", gdp$Export))
cor(gdp$Export, gdp$GDP)
```

```
names(cdc)
hist(cdc$height)
boxplot(cdc$height)
boxplot(cdc$height~ cdc$gender)

pop_mean <- 300
pop_sd <- 10
coke = c(278,289,291,291,291,285,295,278,304,287,291,287,288,300,309,280,294,283,292,306)

sde <- pop_sd / sqrt(length(coke))
z   <- (mean(coke) - pop_mean) / sde
curve(dnorm(x), -3,3)
p   <- (1 - pnorm(abs(z))) * 2


pop_mean = mean(cdc$height)
pop_sd = sd(cdc$height)

set.seed(123)
samp = sample(cdc[cdc$gender == 'm',]$height, 20)
boxplot(samp)
abline(h = pop_mean, col= "red")
sde <- pop_sd / sqrt(length(samp))
z   <- (mean(samp) - pop_mean) / sde

# two sample means are equal
p   <- (1 - pnorm(abs(z))) * 2

# the mean height of the sample is taller than the mean height of the population
p   <- 1- pnorm(z)

z.test <- function(x, pop_mean, pop_sd, side="twoside"){
  sde <- pop_sd / sqrt(length(x))
  z   <- (mean(x) - pop_mean) / sde
  
  switch(side, 
         twoside={
           p   <- (1 - pnorm(abs(z))) * 2
         },
         less={
           p   <- pnorm(z)
         },
         {
           p   <- 1- pnorm(z)
         }
  )
  return(list(z = z , p = p))
}

help(package ="stat")

```

-- http://scikit-learn.org/stable/_static/ml_map.png

```
data(iris)
head(iris)
install.packages("rpart")
library(rpart)
fit = rpart(Species ~ Sepal.Length + Sepal.Width + Petal.Length + Petal.Width, data = iris)
plot(fit, margin =0.1)
text(fit)

install.packages("e1071")
library(e1071)
fit2 = svm(Species ~ Sepal.Length + Sepal.Width + Petal.Length + Petal.Width, data = iris)

```