- Create a new project with the name
`introduction-to-r`

- Open RStudio by clicking on the icon or by selecting it via the start menu
- Click on
`File`

-`New Project...`

and select`New directory`

- Give the directory the name
`introduction-to-r`

and create it as a sub-directory of your*Desktop*folder - Where on your hard disk is the project folder located? Try to locate it with the regular windows file explorer.

- Create a sub-directory
`data`

and`source`

in the project’s root folder. - Download the
*titanic*and the*football*dataset from the course website and place it in the`data`

folder. - In RStudio type
`getwd()`

into the console window. This prints out the full path of your projects root folder.- Type
`list.files("./data")`

into the console window. What’s the meaning of the dot`.`

in the file path? - What’s the output of the call
`list.files("../")`

?

- Type

`helloWorld.R`

)- Click on
`File`

-`New File`

-`R Script`

or use the plus button in the toolbar. - Write
`plot(rnorm(100))`

into the text-editor - Execute the selected line by pressing [Strg]-[Enter] or by clicking on the
`Run`

button in the toolbar. - What’s the purpose of this command? Call the help page for the function
`rnorm`

. *Advanced*: Write a small program which calculates the empricial mean and standard deviation for \(n=10\) random draws from the standard normal distribution.- Use the functions
`mean`

,`sd`

and`rnorm`

- E.g. type
`?mean`

in the console to call the help page for this function - What happens to the mean and deviation if \(n \rightarrow \infty\)? Try this in your program!

- Use the functions
- Save the file (
`File`

-`Save`

) in the`source`

folder of your project. Give it the name`helloWorld.R`

.

Download the script

`kvb.R`

from the course website and save it in the project’s`source`

folder.Install the missing packages

`XML`

and`leaflet`

with the function`install.packages`

`install.packages(c("XML", "leaflet"))`

In your project in RStudio, open the script file and run the code line by line. Does the script terminate without any errors?

*Advanced*- Change the color of the markers from red to green.
- Try to get and visualize data for another city in which
*nextbike*operates (Inside the code, you have to change the link to the nextbike api). - Add a cluster effect to the map (Use the function parameter
`clusterOptions = markerClusterOptions()`

at the right place). - Change the pop-up text of the markers to display some other useful information such as the number of bikes at this place.

Perform the following calcuations using the R console:

- \(34^2 + 12^{-0.8}\)
- \(\ln(4 + \sqrt{12})\)
- \(\frac{2+1}{3+\pi}\)
- \(\ln(e^4)\)

*Advanced*: \(\sqrt{2}^2 - 2 = 0\), right?

- In R, why is
`sqrt(2)^2 - 2`

not exactly equal to zero? - Do you find other examples?

- Have a look at the documentation for the function
`rnorm`

.- How many arguments has the function?
- What are the default arguments of the function?
- Which of the following function calls is not valid? Why?

`rnorm(n = 10) rnorm(10, 2, 4) rnorm(mean = 2) rnorm(sd = 3, mean = 1, n = 3)`

- With the help of the above function calls, explain how R matches
*formal*to*actual*arguments!

- What are the three basic data types? Write down a code example for each of them.
- What’s the difference between
`TRUE`

and`"TRUE"`

? Whats the difference between`pi`

and`"pi"`

? - Use the function
`as.numeric()`

to cast values to a*numeric*type:- What’s the numeric value of
`TRUE`

and`FALSE`

? - Can you cast the character string
`"hi"`

to a numeric value? Try the same with the string`"5"`

. - How can you cast a numeric value to a string? To a logical value?

- What’s the numeric value of

Asign the value \(12\) to a variable with the name

`pi`

- Why is this dangerous?
- Remove the variable by calling the
`rm()`

function with the appropriate argument.

Use the

`c()`

function to store the results from the calculations in exercise*1.4*in a vector . Assign the vector to a variable with the name`values`

.Try to find the name of the built-in functions and answer the following questions:

- What’s the sum and the product of the elements in the vector?
- What is the smallest/ largest value?
- How can you sort the vecor?
- How can you determine the length of the vector?

Call the

`ls()`

function to list all user variables in the global envrionment.- How many variables are listed? Try to answer this question programmatically.
- What is the data type of the object returned by a call of
`ls()`

?

`descriptive.R`

- Open a new script file and save it in the
`source`

folder under the name`descriptive.R`

- Write a program which calculates the mean, the standard deviation, the range, the maximum and the minimum of an arbitrary numeric vector
`x`

- You program should start with the following lines of code:

`# define some arbitrary numeric vector with varying length e.g. x <- c(1, 4, 2, 9) # calculate the statistics`

- Use only the built-in functions
`max()`

,`min()`

,`length()`

and`sum()`

- The range is defined as \(x_{max} - x_{min}\)

- Try to generate the following sequences with the help of the functions
`c()`

,`rep()`

and`seq()`

:- \((1, 2, \dots, 100)\)
- \((-10, -9.5, -9, -8.5, \dots, -4.5, -4)\)
- \((TRUE, FALSE, TRUE, FALSE, TRUE, FALSE)\)
- \(("A", "B", "C", "A", "B", "C", "A", "B", "C")\)
- \((100, 90, 80, \cdots, 10, 0, -10)\)

*Advanced*(Tip: Have a look at the documentation for the function`rep()`

):- \((1, 1, 1, 2, 2, 2, 3, 3, 3, 4, 4, 4, \cdots, 100, 100, 100)\)
- \((1, \dots, 100, 1, \dots, 100, 1, \dots, 100, 1, \dots, 100)\)
- \((1000000, 100000, 10000, 1000, 100, 10, 1)\)

Have a look at the two vectors:

```
x <- c("TRUE", "FALSE", "TRUE", "TRUE")
y <- c("2", "4", "5")
```

Execute the following expressions in R and explain the result.

```
as.numeric(as.logical(x))
is.numeric(y)
is.character(x)
is.logical(as.character(TRUE))
```

Try to guess the result of the following expressions without using a computer

```
is.logical(0)
is.logical(as.logical(0))
is.numeric(as.logical(x))
as.character(1243)
```

Have a look at the two values `x`

and `y`

and the vector `a`

and `b`

```
x <- 9^2
y <- "test"
a <- c(4, 6, 5, 7, 10, 9)
b <- c(4, 6, 2, 7, 2, 3)
```

Execute the following expressions in R and try to explain the result

```
(4 < 5) & (sqrt(x) == 9)
y == "Test" | y == "test"
x < 100 | y != "hallo"
a > 5 & b < 7
all(a > 4 | b < 6)
any(a < 2)
length(a) == length(b)
```

Try to guess the result of the following expressions without using a computer

```
a < 4 & b > a
a == length(b)
any(sqrt(x) == a)
all(a < b)
length(x)
```

- Create a vector of logical values and apply the
`sum()`

and`mean()`

function to it. What do you observe? - With the function
`rnorm()`

, sample \(n = 100\) values from the normal distribution. Count the*relative*and*absolute*number of observations which are- positive
- between \(-1\) and \(1\)
- larger than two times the empirical standard deviation of the sample

*Advanced*: Given the previous three expressions, calculate the*analytical*probability values with the function`pnorm()`

for some random normal variable with \(X \sim N(\mu_x,\sigma_x)\). E.g. calculate the probabilities:- \(P(X > 0)\)
- \(P(-1 \leq X \leq 1)\)
- \(P(X > 2\sigma_x)\)

- What is the keyword for a missing value? Create a vector with numeric values and some missing values.
- Use the function
`is.na()`

on your vector to test for missing values. What is the return type of the function`is.na()`

? - Use the
`sum()`

function together with`is.na()`

to count the number of missing values in the vector. - Have a look at your code in
`descriptive.R`

.- What happens to the code, if the vector
`x`

contains missing values? - Try to rewrite your code such that missing values are handled (E.g. look at the further function arguments of the functions
`mean()`

,`sum()`

, …). - Expand the code by an expression, which counts the number of missing values.

- What happens to the code, if the vector

`.csv`

dataOpen the titanic dataset with a text editor (e.g. right click on the file - `edit with notepad++`

)

- How many variables/columns has the dataset?
- How many passengers are included in the dataset?
- Does the file contain a header line?
- How are the values separated?
- What’s the encoding of the file?

- Open a new script file, save it in
`source`

and give it the name`titanic.R`

. - Use the
`read.csv()`

function with the correct file path, to import the titanic dataset into R (Remember to also include the argument`stringsAsFactors = FALSE`

). - Have a look at each column and determine it’s datatype. You can also use the
`summary()`

or the`head()`

function for this. - Try to answer the following questions
`programmatically`

:- How many passengers and which variables are included in the dataset?
- How many people died on the titanic? How many people survived? Calculate the overal survival rate (E.g. the number of survivors as a fraction of the overall number of passengers).
- How many of the passengers are women?
- How many missing values does the variable
`age`

contain? - What’s the age of the youngest and oldest passenger on the titanic?
- How many passengers are in the first class?

With the titanic dataset and the function `table()`

answer the following questions:

- How many men are in the third class?
- How many people died in the first class? How many in the third class?

In addition, use the functions `prop.table()`

to transform the tables into relative frequency tables:

- Calculate the survival rate separately for each class. Did people from the first class had a higher chance to survive?
- Did women have a higher chance to survive?

- Add a new column
`isMale`

to the dataset which is`TRUE`

if the passenger is male. - Change the data-type of the
`survived`

column from`numeric`

to`logical`

. - Add a new column
`isChild`

to the dataset which is`TRUE`

if`age < 18`

and`FALSE`

else. Are missing values preserved? *Advanced*: Add a new column which is`TRUE`

if the`name`

contains the string`"Miss"`

and`FALSE`

else.- Use the function
`grepl()`

- Did unmarried woman had a greater chance to survive?

- Use the function

Use the function `chisq.test`

to check if there is a significant relationship between the class and the survival rate of a personen.

- Use the
`table`

function to create a contingency table. - Whats the null hypothesis of the test?
- How large is the p-value and what can you conclude?

- Import the football dataset using the
`read.csv2()`

function. Why do you have to use`read.csv2()`

instead of`read.csv()`

? - How many games are in the dataset?
- How many unique countries are included in the dataset?
- How many games from the
`FIFA World Cup`

are included in the dataset? - Think of some questions you want to answer with the dataset and if you can allready answer them with the tools you have learned so far.

`countMissings()`

Write a function `countMissings`

which accepts a numeric vector `x`

as input argument and returns the number of missing values `NA`

in the vector.

Use this template as a start:

`countMissings <- function(x){ # calculate nMissings here # return the number of missing values return(nMissings) }`

Apply the function to the

`age`

variable from the`titanic`

dataset.*Advanced*: If the vector contains*only*missing values, a warning should be printed to the console. Use the function`warning()`

and an`if`

construct for this.

`descriptive.R`

into a functionWrap your code from `descriptive.R`

into a function with the name `descriptive()`

. The function accepts a numeric vector `x`

as input argument, calculates the descriptive statistics and returns them in a *named* vector. Use this template as a start:

```
descriptive <- function(x){
# calculate the descriptive statistics for x here
# return the result
return(result) # result should be a named vector containing the descritpive statistics
}
```

Tip: You can create a named vector like this:

`result <- c(mean = 0.4, sd = 4, range = 2)`

Apply the function

`descriptive()`

to the`survived`

and`pclass`

column from the`titanic`

dataset.*Advanced*: What happens if you apply your function to the`age`

variable which contains missing values. Think of ways to correctly handle missing values (e.g. you could add an additional argument`removeNA`

to your function)*Advanced*: If the type of the vector`x`

is not`numeric`

, the function should terminate with an error (look at the function`stop()`

).

`sapply()`

function- use
`sapply()`

with the`countMissings()`

function from exercise \(4.1\) to count the number of missing values in each column of the`titanic`

dataset.

What’s wrong with the following lines of code? Rewrite the function `mySum`

such that it can be used without errors.

```
mySum <- function(a){# calculates the sum of two numbers a and b
return(a+b)
}
mySum(4)
b <- 6
mySum(2)
```

Look at the following code:

```
norm <- function(x){# calculates the eucledian norm of a vector
xNorm <- sqrt(sum(x^2))
return(xNorm)
}
x <- c(1, 2, 1)
x <- norm(x)
xNorm
x
```

- Does the code terminate without any errors? Where is the mistake? Correct the mistake.
- In this example, what’s the
*formal*and the*actucal*argument of the function`norm()`

? - What’s the value of the variable
`x`

after the code terminates?

`normalize()`

- Write a function
`normalize()`

which standardizes a numeric vector`x`

such that \[ x_{norm} = \frac{x-\bar{x}}{x_{sd}} \]- If the vector contains missing values a warning via the function
`warnings()`

should be printed to the console. - If the vector is not
`numeric`

(e.g. it contains logical values), the function should be terminating with an error. Use the function`stop()`

and`is.numeric()`

.

- If the vector contains missing values a warning via the function
- Rewrite the function
`normalize`

such that the user can pass two parameters`m`

and`s`

with \[ x_{norm} = \frac{x-m}{s} \]- Think of
*downward compability*: A user should still be able to call the function via`normalize(x)`

. You can achieve this by using*default arguments*.

- Think of

- Which methods for extracting values from a vector do you know?
- Sample \(n = 100\) values from the standard normal distribution and subset the sample by selecting
- only positive values
- values between \(-1\) and \(1\)
- the first and the last value
- everything but the first value

Look at the two vectors:

```
x <- c(2, 3, 4, 4)
y <- c(TRUE, FALSE, FALSE, TRUE)
```

Without using a computer: What’s the result of the following expressions?

```
sum(x[y])
sum(x[!y])
sum(y[x])
sum(y[-x])
# advanced
which(x > 3)
which(x[y] > 3)
```

How can you remove missing values from a vector? Write a function `removeNA()`

which takes some numeric vector `x`

as input and returns the vector with missing values removed.

- Find an expression for selecting only non-missing values from the vector
`x`

(e.g. use the function`is.na`

together with extraction method`[]`

) - Inside the function create a variable
`xClean`

containing the subset of`x`

with the missing values removed - Return the vector
`xClean`

A call of this function should look like this:

```
x <- c(2, 3, NA, 4)
removeNA(x)
```

`[1] 2 3 4`

Write a function `negToZero()`

which sets negative numbers in a vector `x`

to \(0\). A call of this function should look like this:

```
x <- c(-10, 3, -2, 3, 4)
negToZero(x)
```

`[1] 0 3 0 3 4`

Write a function `codeToNA()`

which converts some user defined numbers in a vector `x`

into `NA`

s.

- Tip: Use the
`%in%`

operator to update the values inside the vector`x`

. - To understand how the
`%in%`

operator works, have a look at this example:`1:10 %in% c(1,3,5,9)`

A call of this function looks like this:

```
x <- c(2, 3, -99, -999, NA, 4)
codeToNA(x, c(-99, -999))
```

`[1] 2 3 NA NA NA 4`

Write a function `removeOutliers()`

which identifies positive outliers in a numeric vector `x`

.

- Here, a positive outlier \(x_i\) is defined as \(x_i: x_i > \bar{x} + 3*sd(x)\).
- The function should return the vector without outliers.
*Advanced*: Enhance the functionality by allowing the user to specify if only*positive*, only*negative*or both*positive*and*negative*outliers should be removed.

A call of this function looks like this:

```
x <- c(2, 3, 120,1.5, 2, 1, 0, 999)
removeOutliers(x)
```

`[1] 2.0 3.0 120.0 1.5 2.0 1.0 0.0`

*Advanced*: You can also write a function`detectOutliers`

which gives the*indices*of the outliers in a vector. Are there any outliers in the age column of the titanic dataset?

- Add a new column
`ageImputed`

to the dataset which contains the age of the passenger but with`NA`

s replaced by the overall average age (see Mean imputation). - Create a copy of the titanic dataset for which the passengers (e.g. the rows) with a missing value are removed.
- Filter the titanic dataset and select only:
- the survivors
- women in the first class
- male children.

- What is the average age for passengers which have a
`Miss`

in their name (comare with exercise 3.4)? - Use the function
`t.test`

to perform a two sample t-test and check wether the difference in the mean age between Misses and all other passengers is significant. - What’s the meaning of the confidence interval?
- Use the same test but now just use a one-sided test (e.g. test if the difference in the means is less than zero).

- Order the rows of the titanic dataset such that the age is in
*decreasing*order. - What’s the name and age of the youngest/ the oldest passenger? Did he or she survive?
*Advanced*: Select the top \(10\) youngest passengers from each class. How many of them survived?

- Complete the step by step visualization from the slides
- Add additional elements or labels
- Change the colors, the point size or the line type
- Save your plot as a pdf document

Choose a visualization from the examples on the slides and complete the plot, e.g.

- add a title, subtitle, caption
- change the theme
- …

- Form groups of two to four and choose a dataset
- Develope a small research question or replicate a question from the exercises
- In a new .R script file read in the data, clean and transform it
- If needed, apply a regression model or conduct a statistical test
- Create 1 or 2 visualizations and upload the code to ILIAS
- Make sure that your script file contains no errors, is readable and sharable

Use the `matrix`

function and create the following matrics \[
A=
\begin{pmatrix}
2 & 4 \\
1 & 6 \\
\end{pmatrix}
, B =
\begin{pmatrix}
1 & 3 & 9\\
8 & 2 & 4\\
\end{pmatrix}
, C =
\begin{pmatrix}
TRUE & TRUE & FALSE\\
TRUE & FALSE & TRUE\\
\end{pmatrix}
\] Calculate

- \(A*B\)
- \(B'*A\)
- \((A*B*A')^{-1}\).

- Write a function
`myTTest`

which tests, if the mean of two given numeric vectors`x`

and`y`

is statistically different from one another (see here for a detailed explanation)- The input arguments of the function are the vectors
`x`

,`y`

and a significance level`alpha`

- The null hypothesis is: \(H_0: \mu_x = \mu_y\).
- The test value can be calculated as: \[ T = \frac{\bar{x}-\bar{y}}{\sqrt{\frac{1}{n}x_{sd}^2+ \frac{1}{m}y_{sd}^2}} \]
- \(H_0\) is rejected if \(|T| > u_{1-\frac{\alpha}{2}}\)
- \(n\), \(m\) are the length of the vectors \(x\) and \(y\)
- \(u_{1-\frac{\alpha}{2}}\) is the quartile of the normal distribution (see
`qnorm()`

) - The function should return a list with the mean of each of the two vectors, the test value and a logical value indicating the test result

- The input arguments of the function are the vectors
- Compare your results with the built in function
`t.test`

*Advanced*- Calculate p-values or produce a nice output (e.g. with stars indicating the strength of significance)
- If the sample size \(n,m<40\) a warning should be printed (see
`warning()`

)

Write a function `myRegression`

which performs a multivariate linear regression analysis given some outcome `y`

and some design matrix `X`

. The model is given by the equation: \[
y = X\beta + \epsilon,~ \epsilon \sim N(0, \sigma^2)
\] The function should calculate the following statistics:

- The regression coefficients: \(\hat{\beta} = (X'X)^{-1}X'y\)
- The number of observations \(N\) and the number of regressors \(K\)
- The residuals: \(e = y - X\hat{\beta}\)
- The error variance \(\hat{\sigma^2} = \frac{\sum_{i = 1}^{N}{e_i^2}}{N-K}\)
- The coefficient of determination \(R^2 = 1 - \frac{\sum_{i = 1}^{N}{e_i^2}}{\sum_{i = 1}^{N}{(y_i - \bar{y})^2}}\)

The results should be returned using a named list. Check your calculations using the built-in function `lm`

.

*Advanced*: Enhance the function with a t-test for the coefficients and calculate p-values and confidence intervals

*Tip*: R can do matrix arithmetic such as addition, multiplication and inversion: Have a look at `help("%*%")`

and `?solve`

Use the titanic dataset and the examples from to slides:

- Run a simple linear regression model with the formula
`survived ~ ageImputed`

. Is the age significant (`ageImputed`

was calculated in exercise 5.7)? - In addition, include the
`pclass`

and the`sex`

as independent variables. Is the age now significant? - In the model above, what’s the effect of the age on the survival rate (E.g. how much does the probability of survival decreases for passenger who is one year older)?
- Include the
`embarked`

variable. Are there any significant effects? - Use the
`predict.lm`

function to predict the probability of survival for each passenger. Compare the predicitons to the real outcome. How good is the fit? *Advanced*: What’s the probability of survival for a \(20\) year old male in the third class? Use the`predict.lm()`

function with the`newdata`

argument.

Try to squeeze out some information from the `name`

column in the `titanic`

dataset:

- Look for family names and - together with the columns
`embarked`

and`pclass`

- identify family members. - Extract the title (e.g.
*Mr*,*Miss*,*Master*, …) from the name. - What else can you do?

Tip: Install the `stringr`

package, load it with `library(stringr)`

and have a look at the various functions having the naming convention: `str_<action>()`

(e.g. `str_replace()`

, `str_detect()`

).

Use the `ggplot2`

package, the `glm()`

function and the `titanic`

dataset to model and visualize survival rates on the titanic. Use a logistic regression model with the independent variables *age*, *pclass* and *sex* and the dependent variable *survived*.

The final figure could look like this (A script to produce this figures can be found in the scripts section):

A guidance on how to proceed:

- Import the
`titanic`

dataset and use the function`as.factor()`

to transform the*pclass*and the*sex*variable into the`factor`

datatype. - Use the
`glm`

function with the formula:`survived ~ pclass + sex + age + pclass:sex + pclass:age + sex:age`

and the`family = "binomial"`

argument.- with the
`:`

in the formula, interaction effects can be specified - with
`family = "binomial"`

one can specify a logistic regression model

- with the
- Apply the
`summary()`

function to the model object and try to interpretate the coefficients. Why is it important to transform the*pclass*variable to the`factor`

datatype befor applying the model? - Use the model, to predict survival rates over the possible range of
`age`

,`sex`

and`pclass`

- with the
`expand.grid()`

function, create a new`data.frame`

filled with “artifical” passenger data: for each possible outcome of`sex`

and`pclass`

you should vary the`age`

from \(0-70\). - It is important that the new data has the same columns names as the variable names in the model (e.g.
`sex`

,`pclass`

and`age`

).

- use the function
`predict()`

on the model object and the new data to predict the survival rates. - add a new column with the predictions to the
`data.frame`

containing the new passenger data.

- with the
- Use the
`ggplot()`

function to plot the passenger data- Define the asthetics inside
`ggplot()`

with the`aes()`

function. Use the asthetics`x`

,`y`

and`color`

. - Add the trend lines with
`geom_line()`

- Use
`facet_grid(~pclass)`

to create three separate plots - Add a title with
`ggtitle()`

- Define the asthetics inside
*Further steps*: Find out how to add confidence bars to the plot- The
`predict()`

function can return standard errors for the predictions - The
`geom_ribbon()`

function adds an interval arround the trend lines. Use the additional asthetics`ymin`

for the lower confidence bound,`ymax`

for the upper confidence bound and`fill`

for the transparent fill color.

- The