Lecture 1

class: center, middle, inverse, title-slide

# Lecture 1
### Jung-Jin Lee
### Jan 16, 2019

---

## Help on slides

At any time, press `h` to open `Help`.

---

## What is statistics?

- Statistics is the science of learning from data

- The goal of statistics is to summarize data in a way that allows for
easy descriptions or inferences of the data
  - Data visualization and computing are important parts of statistics

- R, a language and environment for statistical computing and graphics, will be used as a main tool throughout the course

---

## Why R?

- Specialized for data analysis

- Many packages have been developed and are available

- Excellent graphics

- Free!

---

## Installing R/RStudio

- To install R, go to https://www.r-project.org/ and follow instruction there
    - Click on CRAN under Download on the left
    - Choose the closest mirror site (e.g. http://lib.stat.cmu.edu/R/CRAN/)
    - Download R for your platform (Windows/Mac/Linux)
    
- To install RStudio (an integrated development environment for R), go to https://www.rstudio.com/ and follow instruction

---

## RStudio IDE overview

---

## R project setup

- Make a directory to be used for class

- File `$\rightarrow$` New Project `$\rightarrow$` Existing Directory `$\rightarrow$` Create Project from Existing Directory

- Start R by opening the .Rproj file

- To create a new .Rmd file, File `$\rightarrow$` New File `$\rightarrow$` R Markdown `$\rightarrow$` (HTML/PDF/Word)

- To produce pdf output, run following (it may take some time):

```r
install.packages("tinytex")
tinytex::install_tinytex()
```
- Useful chunk options: `message = F, echo = F, eval = F`

- Inline coding can be done using a pair of backticks and `r`: ` `r 2+3`\`

---

## Inline/Console output control

<p align = "center"> 
  <img src = chunk_output_inline.png width = "400">
</p>
---

## R as a calculator

Use R console:

```r
5 + 3
```

```
## [1] 8
```

```r
# everything after # (pound sign) is ignored
# useful for comments
2 * 5 # product of 2 and 5
```

```
## [1] 10
```

```r
3^2
```

```
## [1] 9
```

```r
3**2
```

```
## [1] 9
```

---

## Variables

Variables can be used to store numerical values.

- A variable can be a combination of letters (case sensitive), digits, period (.) and underscore (_).
- It must start with a letter or a period. If it starts with a period, it cannot be followed by a digit.
- Reserved words in R, such as `TRUE`, cannot be used as variables.

```r
Num1 <- 5 
Num2 <- 3 
sum_num <- Num1 + Num2
prod.num <- Num1 * Num2
print(sum_num) 
```

```
## [1] 8
```

```r
print(prod.num)
```

```
## [1] 15
```

---

## Characters

Variables can also be used to store character values.

```r
first_name <- "John" # use quotation marks for character strings
last_name <- 'Smith' # single quotation also works
print(first_name) # print() can be omitted, but encouraged
```

```
## [1] "John"
```

```r
print(last_name)
```

```
## [1] "Smith"
```

---

## Logical values

```r
TF1 <- T # upper case T, not t
TF2 <- F # Upper ase F, not f
print(TF1)
```

```
## [1] TRUE
```

```r
print(TF2)
```

```
## [1] FALSE
```

```r
TF3 <- TRUE # can use TRUE instead of T
TF4 <- FALSE # can use FALSE instead of F
print(TF3)
```

```
## [1] TRUE
```

```r
print(TF4)
```

```
## [1] FALSE
```

---

## Logical values, continued

```r
p <- 4; q <- 6 # semicolon (;) can be used to separate lines
call1 <- p > 5
call2 <- q > 5
call3 <- q > 6
call4 <- q >= 6
print(call1)
```

```
## [1] FALSE
```

```r
print(call2)
```

```
## [1] TRUE
```

```r
print(call3)
```

```
## [1] FALSE
```

```r
print(call4)
```

```
## [1] TRUE
```

---

## Combination of logical values

```r
p <- 4; q <- 6 
print(p < 5 & q < 7) # & means "and": TRUE only if both are TRUE
```

```
## [1] TRUE
```

```r
print(p < 5 & q < 5) 
```

```
## [1] FALSE
```

```r
print(p < 5 | q < 5) # | means "or": FALSE only if both are FALSE
```

```
## [1] TRUE
```

```r
print(!(p < 5)) # ! means "not"
```

```
## [1] FALSE
```

---

## Functions

One or more values can produce new one using R functions.

```r
a <- 1; b <- 3 
s <- sum(a, b) # sum() is a function that computes the sum
print(s)
```

```
## [1] 4
```

```r
first_name <- "John" 
last_name <- "Smith"
# paste() puts together multiple character strings
full_name <- paste(first_name, last_name) 
print(full_name)
```

```
## [1] "John Smith"
```

For detailed usage of a function, type `help(function_name)`, e.g. `help(paste)` or `?function_name`, e.g. `?paste`.

---

## Vectors

Multiple numerical values or characters can be saved as a single variable using an R function `c()`.

```r
vec1 <- c(2, 3, 5, 7, 1, 4)
print(vec1)
```

```
## [1] 2 3 5 7 1 4
```

```r
vec2 <- c("Joe", "waited", "for", "the", "train")
print(vec2)
```

```
## [1] "Joe"    "waited" "for"    "the"    "train"
```

```r
vec3 <- vec2 %in% c("Joe", "for") # %in% determines membership
print(vec3)
```

```
## [1]  TRUE FALSE  TRUE FALSE FALSE
```

---

## Functions applied to a vector -- part I

```r
length(vec1)
```

```
## [1] 6
```

```r
sum(vec1)
```

```
## [1] 22
```

**Exercise**: sort the numbers 2, 3, 5, 7, 1, 4 from the smallest to the largest and vice versa.

```r
sort(vec1)
```

```
## [1] 1 2 3 4 5 7
```

```r
sort(vec1, decreasing = T)
```

```
## [1] 7 5 4 3 2 1
```

---

## Functions applied to a vector -- part II

```r
collapse1 <- paste(vec2, collapse = " "); print(collapse1)
```

```
## [1] "Joe waited for the train"
```

```r
collapse2 <- paste(vec2, collapse = "_"); print(collapse2)
```

```
## [1] "Joe_waited_for_the_train"
```

**Exercise**: produce the following output

```
## [1] "Joewaitedforthetrain"
```

```r
collapse3 <- paste(vec2, collapse = ""); print(collapse3)
```

```
## [1] "Joewaitedforthetrain"
```

---

## Functions applied to a vector -- part III

```r
print(vec1)
```

```
## [1] 2 3 5 7 1 4
```

Which elements are greater than 3?

```r
vec4 <- vec1 > 3
print(vec4)
```

```
## [1] FALSE FALSE  TRUE  TRUE FALSE  TRUE
```

How many elements of `vec1` are greater than 3?

```r
sum(vec4) # in R, TRUE is 1, FALSE is 0
```

```
## [1] 3
```

---

## Vector manipulation

Use brackets `[]` to extract components of a vector.

```r
a <- vec1[3]
print(a)
```

```
## [1] 5
```

```r
dm <- vec2[c(1, 5)]
print(dm)
```

```
## [1] "Joe"   "train"
```

**Exercise**: extract the last element of `vec1` without viewing its elements.

```r
vec1[length(vec1)]
```

```
## [1] 4
```

---

## Special vectors -- part I

**Exercise**: compute the sum `$1 + 2 + 3 + \cdots + 10$`.

```r
w1 <- c(1, 2, 3, 4, 5, 6, 7, 8, 9, 10)
sum(w1)
```

```
## [1] 55
```

Colon (:) can be used to generate a vector consisting of consecutive numbers.

```r
w2 <- 1:10
print(w2)
```

```
##  [1]  1  2  3  4  5  6  7  8  9 10
```

```r
sum(w2) 
```

```
## [1] 55
```

---

## Special vectors -- part II

**Exercise**: compute the sum `$2 + 4 + 6 +\cdots + 20$`.

```r
# one can use a function seq()
# type ?seq to get help
w3 <- seq(2, 20, by = 2)
sum(w3)
```

```
## [1] 110
```

Alternatively, one can use the previous vector:

```r
w4 <- 2*w1 # product of a single number and a vector
print(w4)
```

```
##  [1]  2  4  6  8 10 12 14 16 18 20
```

```r
sum(w4)
```

```
## [1] 110
```

---

## Recycling in R

Operation between a single value and a vector.

```r
num3 <- 3
vec5 <- 1:5
vec6 <- vec5 + num3
print(vec6)
```

```
## [1] 4 5 6 7 8
```

```r
vec7 <- paste0("Visitor_", vec5)
print(vec7)
```

```
## [1] "Visitor_1" "Visitor_2" "Visitor_3" "Visitor_4" "Visitor_5"
```

```r
vec8 <- 5 + 2*c(-1, 1)
print(vec8)
```

```
## [1] 3 7
```

---

## Data frame

Vectors of an equal length can be combined to form a data frame.

```r
# use of the function data.frame()
first_name <- c("Lisa", "John", "Chuck", "Matt")
last_name <- c("Simpson", "Smith", "Williams", "June")
age_yrs <- c(8, 42, 81, 23)
book <- data.frame(first = first_name,
                   last = last_name,
                   age = age_yrs)
print(book)
```

```
##   first     last age
## 1  Lisa  Simpson   8
## 2  John    Smith  42
## 3 Chuck Williams  81
## 4  Matt     June  23
```

```r
dim(book) # dimensions of a data frame: dim()
```

```
## [1] 4 3
```

---

## Handling data frames

```r
# extract a single element from a data frame
book[2, 3]
```

```
## [1] 42
```

```r
# extract a column: use $
age_extracted <- book$age
print(age_extracted)
```

```
## [1]  8 42 81 23
```

```r
# extract a row
book[4, ]
```

```
##   first last age
## 4  Matt June  23
```

---

## Retrieving a column from a data frame

```r
# use column number
method1 <- book[,1]
print(method1)
```

```
## [1] Lisa  John  Chuck Matt 
## Levels: Chuck John Lisa Matt
```

```r
# use "$" to extract a column
method2 <- book$first
print(method2)
```

```
## [1] Lisa  John  Chuck Matt 
## Levels: Chuck John Lisa Matt
```

---

## Adding a variable in a data frame

```r
gender <- c("Female", "Male", "Male", "Unknown")
book$sex <- gender
print(book)
```

```
##   first     last age     sex
## 1  Lisa  Simpson   8  Female
## 2  John    Smith  42    Male
## 3 Chuck Williams  81    Male
## 4  Matt     June  23 Unknown
```

Recycling applies to a data frame

```r
book$remark <- "friend"
print(book)
```

```
##   first     last age     sex remark
## 1  Lisa  Simpson   8  Female friend
## 2  John    Smith  42    Male friend
## 3 Chuck Williams  81    Male friend
## 4  Matt     June  23 Unknown friend
```

---

## Reading a data file

Download a [file](heights.txt) to be used in an example (Chrome users: Menu `$\rightarrow$` More Tools `$\rightarrow$` Save Page As).

```r
# heights.txt is a space-delimited file 
# consisting of 1375 observations of mom/daughter age height pairs
# file path `file = "heights.txt"` below should be adjusted!
# Mac users: Finder -> Right click -> Option -> Copy as pathname
d <- read.table(file = "heights.txt", header = TRUE, sep = " ")
```

A glance at a data frame:

```r
dim(d) # dimension
```

```
## [1] 1375    2
```

```r
names(d) # variable(column) names
```

```
## [1] "Mheight" "Dheight"
```

---

## Inspecting a data frame

```r
head(d) # first few rows (6 rows by default)
```

```
##   Mheight Dheight
## 1    59.7    55.1
## 2    58.2    56.5
## 3    60.6    56.0
## 4    60.7    56.8
## 5    61.8    56.0
## 6    55.5    57.9
```

```r
tail(d) # last few rows
```

```
##      Mheight Dheight
## 1370    69.5    70.4
## 1371    69.1    70.1
## 1372    65.0    71.6
## 1373    66.3    71.4
## 1374    70.8    71.0
## 1375    63.0    73.1
```

---

## Histogram

The first step of data analysis is often data visualization. A histogram is a good tool to understand the range and frequency of given data.

.pull-left-code[
Instead of using graphic feature from base R, we will use a package developed especially for visualization.

```r
install.packages("tidyverse")
library(tidyverse)
```

In fact, we need only `ggplot2`, which is one of packages contained in `tidyverse`.

```r
g1 <- ggplot(d, aes(x = Mheight)) + 
  geom_histogram()
print(g1)
```
]

.pull-right-plot[
<img src="Cabrini_2019_Lecture_1_files/figure-html/unnamed-chunk-49-1.png" style="display: block; margin: auto;" />
]