1_basics_solutions.Rmd

---
title: "Introduction to R for Biostatistics 1"
output: html_document
---

```{r global_options, include=FALSE}
library(dplyr)
```

##In-class worksheet 1

**29 Feb to 4 Mar, 2016**

We will use R in this class mainly via R Markdown documents. R Markdown documents are documents that combine text, R code, and R output, including figures. They are a great way to produce self-contained and documented statistical analyses. 

In this first worksheet, you will learn how to do some basic markdown editing and some simple data manipulation in R. After you have made a change to the document, press *Knit HTML* in R Studio and see what kind of a result you get. In addition, you should enter the code provided during the instructions part into the *Console* window below. 

## Basic Markdown editing

### Instructions

Try out basic R Markdown features. You may know the Markdown language from editing wikis. Write some text that is bold, and some that is in italics. Make a numbered list and a bulleted list. Make a nested list. Write a short formula. Use the hand out for reference.

### Your assignments

This text is **bold.**

This text is *in italics.*

A numbered list:

1. Item 1
2. Item 2
3. Item 3

A bulleted list:

- Item 1
- Item 2
- Item 3

A nested list:

1. Item 1
    - Item 1.1. Note that 4 spaces are required for the nesting to work properly.
    - Item 1.2
2. Item 2


Formula:
$$ x = \sqrt{y}$$


## Variables, Assignments, Indexing

###Instructions

Variables in R have a name, which typically starts with a letter, is lower case and cannot contain spaces. Variables can be assigned scalar numbers. Then we can perform calculations with the variables instead of the numbers themselves. For example:

```{r}
x <- 5
y <- 7
z <- x * y
z
```

Variables can also be assigned vectors (i.e. "lists") of scalar numbers. There are special functions that allow you to quickly:  

```{r, eval=FALSE}
x <- c(1,5,9,12)        # create a vector with specified numbers
y <- 1:5                # create a vector containing the numbers 1 to 5
z <- rep(0,5)           # create a vector with all zeros
w <- seq(0,10,by=2)     # create a vector with increments of 2
```

We can use the function length to find how many elements there are in a variable:

```{r}
x <- seq(0,20,by=3)
length(x)
```

To extract the values stored at some positions of a vector variable, we can use indexing:

```{r, eval=FALSE}
x <- 1:10
x[2]              # get the 2nd element
x[c(2,3)]         # get the 2nd and 3rd element
x[-1]             # get all but the 1st element
x[11] <- 11       # add a 11th element 
```

There is also logical indexing, which returns you all entries fullfilling a certain condition.

```{r}
x <- 1:10
x[x>5]              # get all elements large than 5

```

You can also store numbers in an array or matrix.

```{r}
A = matrix(seq(1,9,1), nrow=3, ncol=3)
A
```

Elements are indexed by a row and column index. Row comes first. If you omit the index, the entire row/column is returned. 

```{r}
A = matrix(seq(1,9,1), nrow=3, ncol=3)
A[1,]
```


###Your assignments

If you want to try some code before putting it into the Markdown document, you can run it in the Console window below. After you hit enter, R will execute your statements. To look at a variable, just type its name and it enter. Alternatively, you can use the variable browser on the right. If you need help, just type a ? before the name  function. The help window will be shown on the right. You can also use this to explore additional options, which you may need for some of the assignments.

Write code to create a vector with 5 ones and display it.

```{r}
x <- rep(1,5)
x
```

Write code to create a vector with the numbers 5, 10, 15 and so on up to 100.

```{r}
x <- seq(5,100,by=5)
x
```

Write code to create the vector `r c(1, 2, 3, 1, 2, 3, 1, 2, 3)` without having to specify all individual elements.

```{r}
x <- rep(c(1,2,3), 3)
x
```

Write code to create the vector `r c(1, 1, 1, 2, 2, 2, 3, 3, 3)` without having to specify all individual elements. Use ?rep for help.

```{r}
x <- rep(c(1,2,3), each=3)
x
```

What is the difference between the two multiplication operators for matrices? 

```{r}
A <- matrix(seq(1,9,1), nrow=3, ncol=3)

A*A
A%*%A

```

Explore the use of *rowSums* and *columnSums*.

```{r}
A <- matrix(seq(1,9,1), nrow=3, ncol=3)

rowSums(A)

```