hw1.Rmd

---
title: "Homework #1"
author: "Ming Chen & Wenqiang Feng"
date: "2/2/2017"
output: html_document
---
## You can also get the [PDF format](./pdf/HW1.pdf) of Wenqiang's Homework.

#### Required library
```{R message=F,warning=F}
library(histogram)
library(plyr)
```
#### Load data
```{R message=F,warning=F}
homeownership = read.table("./data/ex3-11.TXT", header = T)
hiv = read.table("./data/ex3-76.TXT", header = T)
```

## Q 3.11(a)
```{R}
## X1985
par(mfrow=c(3,1))
hist(homeownership$X1985, freq = F, right = F, ylim = c(0, 0.12), 
     xlim = c(30, 100), xlab = "1985", ylab = "Relative Frequency", 
     main = "", breaks = 20)
## X1996
hist(homeownership$X1996, freq = F, right = F, ylim = c(0, 0.12), 
     xlim = c(30, 100), xlab = "1996", ylab = "Relative Frequency", 
     main = "", breaks = 20)
## X2002
hist(homeownership$X2002, freq = F, right = F, ylim = c(0, 0.12), 
     xlim = c(30, 100), xlab = "2002", ylab = "Relative Frequency", 
     main = "", breaks = 20)
```

## Q 3.11(b)
The three histograms have similar shape. The average homeownship rate has increased since 1985.

```{R}
colMeans(homeownership[,2:4])
```


## Q 3.11(c)
Increases in families incomes so more people can purchase homes.

## Q 3.11(d)
The average homeship rate increases from 65.87% to 69.44% from 1985 to 2002. This is very small inscrease in a long time period. The Congress should write laws to increase tax deductions so that more people can purchase homes.

## Q 3.12 

Stem-and-leaf plots

* Year 1985
```{R}
stem(homeownership$X1985)
```

* Year 1996
```{R}
stem(homeownership$X1996)
```

* Year 2002
```{R}
stem(homeownership$X2002)
```

## Q 3.13: Descriptions of the stem-and-leaf plots

Both the stem-and-leaf and histogram for all three years are asymmetrical, unimodal and left skewed.

## Q 3.36(a)

Boxplots
```{R}
boxplot(homeownership$X1985, xlab="1985", ylim=c(30, 80))
boxplot(homeownership$X1996, xlab="1996", ylim=c(30, 80))
boxplot(homeownership$X2002, xlab="2002", ylim=c(30, 80))
```

Three boxplots are all asysmmetric and left skewed.

## Q 3.36(b)
Boxplots give the same information from the stem-and-leaf and histograms in 3.11: asysmmetric and left skewed data for all three years.

## Q 3.37

* Mean, median and standard deviation

```{R}
colMeans(homeownership[,2:4])
```

* Median
```{R}
colwise(median)(homeownership[,2:4])
```

* Standard deviation
```{R}
colwise(sd)(homeownership[,2:4])
```

## Q 3.37(a)

The __median__ is more approriate than the mean for these data sets, because the data sets are skewed

## Q 3.37(b)

The variability continously descreased since 1985. 

## Q 3.38

```{R}
y = c(homeownership$X1985, homeownership$X1996, homeownership$X2002)
x = rep(c("X1985", "X1996", "X2002"), each=nrow(homeownership))
boxplot(y~x)
```

## Q 3.38(a)

The median hownownership rate continously increased from 1985 to 2002

## Q 3.38(b)
The variation hownownership rate continously decreased from 1985 to 2002.

## Q 3.38(c)

* Yes. 
* State 9, 33, 12 are extremely low in homeownership rate in 1985.
* State 9, 12, 33 are extremely low in homeownership rate in 1996.
* State 9, 33, 12 are extremely low in homeownership rate in 2002.

## Q 3.38(d)

No.

## 3.76(a)

Mean, median and standard deviation
```{R}
data.frame(mean=mean(hiv$HIV_RNA), 
           median=median(hiv$HIV_RNA),
           std=sd(hiv$HIV_RNA))
```

## 3.76(b)

25%, 50% and 75% percentiles
```{R}
quantile(hiv$HIV_RNA)[2:4]
```

## 3.76(c)

* boxplot
```{R}
boxplot(hiv$HIV_RNA, main="HIV RNA")
```

* histogram
```{R}
hist(hiv$HIV_RNA, xlab="HIV RNA", main="", 
     ylim=c(0,20), breaks=10)
```

## 3.76(d)

The distribution is unimodal and right skewed.