1 R-Package ourdata

The R package ourdata was created for Data Science courses at the Fresenius University of Applied Sciences. It contains most of the datasets used for practice purposes, as well as some self-programmed functions with which this data can be manipulated and plots can be generated.

1.1 Data data

The R package ourdata contains the following data:

  • fragebogen
    • Head circumference and other features from student surveys.
    • Age, gender, math grade, expected grade, fear, interest, practice
  • hdi
    • Worldwide Human Development Index.
  • imr
    • Infant mortality rates worldwide.
  • kirche
    • Church exits in Germany from 2017 to 2020.
  • koelsch
    • Consumption of Cologne beer (Koelsch) from 2017 to 2020.
  • oecd_preventable
    • OECD preventable mortality data from 2010 onwards.
    • Standardized death rates per 100,000 inhabitants across OECD countries.

With the function help() you can display help pages for all datasets. E.g. help(fragebogen) explains the content of the data package fragebogen.

1.2 Functions functions

The R package ourdata contains the following functions:

  • combine(x, y, ...)
    • Combines two datasets using ID and foreign key matching.
  • ourdata()
    • Prints a welcome message.
  • plotter(...)
    • Draws various plots interactively with variable data.
  • transformer(x, ...)
    • Transforms values of type char into numeric values,
    • e.g. female to 1, male to 2 and divers to 3.

With the function help() you can display help pages for all functions. E.g. help(plotter) explains the functionality of the function plotter().

2 Data Science Courses

In the Data Science courses at the Fresenius University of Applied Sciences, we have covered many topics of data analysis and examined some technical applications more closely. The focus was on R, a statistical programming language, which was also used to create this document.

Course materials include lecture slides as well as all R scripts and other materials. Here you will find plots and statistical methods and their R code presented in an appealing way. The code is waiting for you to try it out!

2.1 Plots plots

In R or RStudio, you can use various plot types for visualization. The function plotter() helps you create all plots (except the pie chart) with your own data.

Fig. 2.1a: Heatmap

Fig. 2.1a: Heatmap

Here is a selection of plot types with the corresponding code:

2.1.1 Bar Plot

The bar plot illustrates the connection between a numerical and a categorical variable. The bar plot displays each category as a bar and reflects the corresponding numerical value with the size of the bar.

# Creating bar plot
barplot(kirche$Austritte, kirche$Jahr, main = "Church Exits", col.main = "white", col.lab = "white", yaxt = "n", ylab = "Exits (per 1,000)", xlab = "Years", names = c("2017", "2018", "2019", "2020"))

# Improving labeling for x and y axis and adapt color scheme for dark theme
axis(1, at = 1:4, lwd = 3, lwd.ticks = 3, col = "white", col.ticks = "white", col.lab = "white", col.axis = "white")
ypos <- seq(0, 600000, by = 100000)
axis(2, at = ypos, labels = sprintf("%1.0f", ypos), lwd = 0.5, lwd.ticks = 1, col = "white", col.ticks = "white",  col.axis = "grey")

Error : The fig.showtext code chunk option must be TRUE

2.1.2 Box Plot

The box plot shows the distribution of a numerical variable based on five summary statistics: - minimum non-outlier - first quartile - median - third quartile - maximum non-outlier

Box plots also show the positioning of outliers and whether the data is skewed.

# Creating box plot
boxplot(koelsch$Koelsch, main = "Koelsch Consumption", col.main = "white", col.lab = "white", yaxt = "n", ylab = "Koelsch Consumption in Mil. Liters", xlab = "over the period 2017 to 2020", names = "2020")

# Improving labeling for y axis and adapt color scheme for dark theme
ypos <- seq(160000000, 200000000, by = 10000000)
axis(2, at = ypos, labels = sprintf("%1.0fM.", ypos/1000000), lwd = 0.5, lwd.ticks = 1, col = "white", col.ticks = "white",  col.axis = "grey")

Error : The fig.showtext code chunk option must be TRUE

2.1.3 Density Plot

The density plot shows the distribution of a numerical variable over a continuous interval. Peaks of a density plot visualize where the values of numerical variables concentrate.

# Creating density plot
plot(density(fragebogen$alter), main = "Age Distribution in Course", col.main = "white", col.lab = "white", yaxt = "n", ylab = "Persons (Density)", xlab = "Age (in years)")

# Improving labeling for y axis and adapt color scheme for dark theme
ypos <- c(0, 0.01, 0.02, 0.03, 0.04, 0.05, 0.06)
axis(2, at = ypos, labels = sprintf("%1.0fP", ypos*50), lwd = 0.5, lwd.ticks = 1, col = "white", col.ticks = "white",  col.axis = "grey")

Error : The fig.showtext code chunk option must be TRUE

2.1.4 Heatmap

A heatmap visualizes individual values of a matrix with colors. More frequent values are typically displayed by lighter reddish colors and less frequent values are typically displayed by darker colors.

data <- matrix(rnorm(81, 0, 9), nrow = 9, ncol = 9)     # Create example data
colnames(data) <- paste0("Column ", 1:9)                # Set column names
rownames(data) <- paste0("Row ", 1:9)                   # Set row names

# Creating heatmap
heatmap(data, main = "Heatmap", col.main = "white", col.lab = "white")
Error : The fig.showtext code chunk option must be TRUE
Error : The fig.showtext code chunk option must be TRUE
Error : The fig.showtext code chunk option must be TRUE

2.1.5 Histogram

The histogram groups continuous data into ranges and displays this data as bars. The height of each bar shows the number of observations in each range.

# Creating histogram
hist(fragebogen$kopf, main = "Head Circumferences", col.main = "white", col.lab = "white", ylab = "Persons (Count)", xlab = "Head Circumference (in cm)")

Error : The fig.showtext code chunk option must be TRUE

2.1.6 Line Plot

The line plot visualizes values along a sequence (e.g. over time). Line plots consist of an x-axis and a y-axis. The x-axis typically shows the sequence and the y-axis shows the values that correspond to each point in the sequence.

# Creating line plot
plot(fragebogen$note_mathe, type = "l", main = "Math Grades", ylab = "Grades", xlab = "Person x",  yaxt = "n", col.main = "white", col.lab = "white")

# Improving labeling for y axis and adapt color scheme for dark theme
ypos <- c(2, 3, 4, 5)
axis(2, at = ypos, labels = sprintf("%1.0f", ypos), lwd = 0.5, lwd.ticks = 1, col = "white", col.ticks = "white", col.lab = "grey", col.axis = "white")

Error : The fig.showtext code chunk option must be TRUE

2.1.7 Pairs Plot

The pairs plot is a plot matrix that consists of scatter plots for each variable combination of a data frame.

# Creating pairs plot
pairs(data.frame(fragebogen$interesse, fragebogen$note_annahme), main = "Relationship Interest and Expected Grade", labels = c("Interest", "Expected Grade"), col.main = "white", col.lab = "white")

Error : The fig.showtext code chunk option must be TRUE
Error : The fig.showtext code chunk option must be TRUE
Error : The fig.showtext code chunk option must be TRUE
Error : The fig.showtext code chunk option must be TRUE

2.1.8 Qqplot

A QQplot (or Quantile-Quantile plot) determines whether two data sources come from a common distribution. QQplots plot the quantiles of the two numerical data sources against each other. If both data sources come from the same distribution, the points fall on an angle of 45°.

# Creating qqplot
qqplot(fragebogen$geschlecht, fragebogen$note_mathe, main = "Gender and Math Grade", yaxt = "n", ylab = "Math Grade", xaxt = "n", xlab = "Gender (1 'female', 2 'male')", col.main = "white", col.lab = "white")

# Improving labeling for x and y axis and adapt color scheme for dark theme
xpos <- c(1, 2)
axis(1, at = xpos, labels = sprintf("%1.0f", xpos), lwd = 0.5, lwd.ticks = 1, col = "white", col.ticks = "white", col.lab = "grey", col.axis = "white")
ypos <- c(2, 3, 4 , 5)
axis(2, at = ypos, labels = sprintf("%1.0f", ypos), lwd = 0.5, lwd.ticks = 1, col = "white", col.ticks = "white", col.lab = "grey", col.axis = "white")

Error : The fig.showtext code chunk option must be TRUE

2.1.9 Scatter Plot

The scatter plot displays two numerical variables with points. Each point shows the value of one variable on the x-axis and the value of the other variable on the y-axis.

# Combine data
df <- combine(imr$name, hdi$country, imr$value, hdi$hdi, col1 = "Country", col2 = "IMR", col3 = "HDI")
'data.frame':   175 obs. of  3 variables:
 $ Country: chr  "Afghanistan" "Central African Republic" "Niger" "Chad" ...
 $ IMR    : num  106.8 84.2 68.1 67 65.3 ...
 $ HDI    : num  0.496 0.381 0.377 0.401 0.438 0.413 0.588 0.446 0.427 0.574 ...
# Creating scatter plot
plot(df$HDI, df$IMR, main = "Influence of HDI on IMR", ylab = "IMR", xlab = "HDI", col.main = "white", col.lab = "white")
Error : The fig.showtext code chunk option must be TRUE

2.1.10 Pie Chart

Pie charts are widely used, but have some disadvantages:

  • Differences between proportional values are less recognizable, since the area of the circle segments must be compared
  • with many categories, the representation quickly becomes confusing
  • very small proportional values often cannot be displayed in pie charts

Due to these disadvantages, the use of pie charts is only recommended in rare cases; usually dot plots or bar plots provide better representations.

# Creating labels with total and percentage
pie_labels <- paste0(kirche$Austritte, " (", round(100 * kirche$Austritte/sum(kirche$Austritte), 2), "%)")

# Creating pie chart
pie(kirche$Austritte, main = paste0("Church Exits per Year (total ", sum(kirche$Austritte), ")"), labels = pie_labels, col = c("white", "lightblue", "mistyrose", "brown"))

# Creating legend
legend("topleft", legend = c("2017", "2018", "2019", "2020"), fill =  c("white", "lightblue", "mistyrose", "brown"))

Error : The fig.showtext code chunk option must be TRUE

2.1.11 Venn Diagram

A Venn diagram (or set diagram; logic diagram) illustrates all possible logical relationships between specific data characteristics. Each characteristic is represented as a circle, with overlapping parts of the circles representing elements that have both characteristics simultaneously.

# Creating triple Venn diagram
draw.triple.venn(area1 = koelsch$Koelsch[4], area2 = kirche$Austritte[4], area3 = 1000000, n12 = 220000, n23 = 50000, n13 = 600000, n123 = 40000, main = "Koelsch -> Church Exit -> Cologne?", fill = c("yellow", "brown", "blue"), category = c("Koelsch", "Church", "Cologne"), main.col = "white", sub.col = "white", col = "white")

2.2 Data Mining data science

The methods of data mining can basically be divided into the groups classification, prediction, segmentation and dependency discovery. Algorithms are used for this purpose.

An algorithm is a formal instruction for solving instances of a specific problem class. 1

Fig. 2.2a: Data Mining Groups

Fig. 2.2a: Data Mining Groups

Here you will find the data mining methods from the lectures, with the corresponding code:

2.2.1 Correlation Analysis

If you want to investigate a relationship between two metric variables, for example between the age and weight of children, you calculate a correlation. This consists of a correlation coefficient (rho for Spearman) and a p-value.

The correlation coefficient indicates the strength and direction of the relationship. It ranges between -1 and 1. A value near -1 indicates a strong negative relationship (e.g. “More distance traveled by car, less fuel in the tank”). A value near 1 indicates a strong positive relationship (e.g. “more feed, fatter cows”). No relationship exists when the value is close to 0.

The p-value indicates whether there is a significant relationship. p-values less than 0.05 are considered statistically significant.

# Combining both lists with 'SQL JOIN'
imr_hdi <- sqldf('SELECT imr.name AS "country", imr.value As "imr", hdi.hdi AS "hdi" FROM imr INNER JOIN hdi ON imr.name = hdi.country ORDER BY imr.value DESC')

# Scatter plot
plot(imr_hdi$imr ~ imr_hdi$hdi, main = "HDI IMR Correlation", ylab = "Infant Mortality (per 1,000)", xlab = "Human Development Index", xlim = range(0:1), ylim = range(1:110))

# Quantify relationships using Spearman correlation function
cor.test(imr_hdi$imr, imr_hdi$hdi, method="spearman", exact=FALSE)
Error : The fig.showtext code chunk option must be TRUE

    Spearman's rank correlation rho

data:  imr_hdi$imr and imr_hdi$hdi
S = 1719986, p-value < 2.2e-16
alternative hypothesis: true rho is not equal to 0
sample estimates:
       rho 
-0.9256444

2.2.2 Linear Regression Analysis

Linear regression is one of the most useful tools in statistics. Regression analysis allows you to estimate relationships between parameters and thus provide an explanatory model for the occurrence of certain phenomena. True causality is not revealed by statistical analyses of this kind, but the results from such analyses can provide clues in this direction. 2

# Creating a comparable dataset with IMR and HDI using the 'combine' function from the R package 'ourdata'
df <- combine(imr$name, hdi$country, imr$value, hdi$hdi, col1 = "Country", col2 = "IMR", col3 = "HDI")

# Creating linear model with 'lm'
mdl <- lm(IMR ~ HDI, data=df)

# Showing model's summary
summary(mdl)

# Calculating the p-value for 'HDI'
matCoef <- summary(mdl)$coefficients
pval <- matCoef["HDI", 4]
print(paste0("The effect of HDI on IMR is statistically significant p = ", round(pval, 2), " (", pval, ")."))

# Creating plot
plot(df$HDI, df$IMR, xlab = "Predictor", ylab = "Result", col = "darkblue", pch = 16, main = "Linear Regression")

# Creating regression line
abline(mdl, col = "darkred")

'data.frame':   175 obs. of  3 variables:
 $ Country: chr  "Afghanistan" "Central African Republic" "Niger" "Chad" ...
 $ IMR    : num  106.8 84.2 68.1 67 65.3 ...
 $ HDI    : num  0.496 0.381 0.377 0.401 0.438 0.413 0.588 0.446 0.427 0.574 ...

Call:
lm(formula = IMR ~ HDI, data = df)

Residuals:
    Min      1Q  Median      3Q     Max 
-24.833  -4.900   0.041   5.132  59.646 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  103.266      3.467   29.78   <2e-16 ***
HDI         -113.229      4.733  -23.92   <2e-16 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 9.45 on 173 degrees of freedom
Multiple R-squared:  0.7679,    Adjusted R-squared:  0.7666 
F-statistic: 572.4 on 1 and 173 DF,  p-value: < 2.2e-16

[1] "The effect of HDI on IMR is statistically significant p = 0 (9.32053277007795e-57)."
Error : The fig.showtext code chunk option must be TRUE

2.2.3 Market Basket Analysis

Market basket analysis can lead to the discovery of associations and correlations between elements in huge transactional or relational datasets.

Finding connections between different items that customers put in their “shopping baskets” is a common application of the analysis. Knowledge of these associations can be helpful for retailers or marketers to develop marketing strategies. This happens by gaining insights into which items are frequently purchased together by customers.

For example, if customers buy milk, how likely is it that they will also buy bread (and which type of bread) on the same trip to the supermarket? This information can lead to increased sales by helping retailers engage in selective marketing and plan their sales floor.

# Loading libraries
library(arules)     # Package with mining datasets and association rules
library(datasets)   # OpenIntro datasets

# Loading data frame
data(Groceries)

# Creating frequency plot for the top 20 items
itemFrequencyPlot(Groceries, topN = 20, type = "absolute", horiz = TRUE)
Error : The fig.showtext code chunk option must be TRUE

# Searching for milk
itemFrequency(Groceries)[grep("milk", itemLabels(Groceries))]
    whole milk    butter milk       UHT-milk condensed milk 
    0.25551601     0.02796136     0.03345196     0.01026945 
# Deriving the rules
rules <- apriori(Groceries, parameter = list(supp = 0.001, conf = 0.8))
Apriori

Parameter specification:
 confidence minval smax arem  aval originalSupport maxtime support minlen
        0.8    0.1    1 none FALSE            TRUE       5   0.001      1
 maxlen target  ext
     10  rules TRUE

Algorithmic control:
 filter tree heap memopt load sort verbose
    0.1 TRUE TRUE  FALSE TRUE    2    TRUE

Absolute minimum support count: 9 

set item appearances ...[0 item(s)] done [0.00s].
set transactions ...[169 item(s), 9835 transaction(s)] done [0.00s].
sorting and recoding items ... [157 item(s)] done [0.00s].
creating transaction tree ... done [0.00s].
checking subsets of size 1 2 3 4 5 6 done [0.01s].
writing ... [410 rule(s)] done [0.02s].
creating S4 object  ... done [0.00s].
# Showing the top 5 rules (only 2 decimal places)
options(digits=2)
inspect(rules[1:5])
    lhs                         rhs            support confidence coverage lift
[1] {liquor, red/blush wine} => {bottled beer} 0.0019  0.90       0.0021   11.2
[2] {curd, cereals}          => {whole milk}   0.0010  0.91       0.0011    3.6
[3] {yogurt, cereals}        => {whole milk}   0.0017  0.81       0.0021    3.2
[4] {butter, jam}            => {whole milk}   0.0010  0.83       0.0012    3.3
[5] {soups, bottled beer}    => {whole milk}   0.0011  0.92       0.0012    3.6
    count
[1] 19   
[2] 10   
[3] 17   
[4] 10   
[5] 11   
rules <- sort(rules, by="confidence", decreasing = TRUE)
rules <- apriori(Groceries, parameter = list(supp = 0.001, conf = 0.8, maxlen = 10))
Apriori

Parameter specification:
 confidence minval smax arem  aval originalSupport maxtime support minlen
        0.8    0.1    1 none FALSE            TRUE       5   0.001      1
 maxlen target  ext
     10  rules TRUE

Algorithmic control:
 filter tree heap memopt load sort verbose
    0.1 TRUE TRUE  FALSE TRUE    2    TRUE

Absolute minimum support count: 9 

set item appearances ...[0 item(s)] done [0.00s].
set transactions ...[169 item(s), 9835 transaction(s)] done [0.00s].
sorting and recoding items ... [157 item(s)] done [0.00s].
creating transaction tree ... done [0.00s].
checking subsets of size 1 2 3 4 5 6 done [0.01s].
writing ... [410 rule(s)] done [0.02s].
creating S4 object  ... done [0.00s].
# Loading package with visualization association rules
library(arulesViz)

# Matrix calculations
subset.matrix <- is.subset(rules, rules)
subset.matrix[lower.tri(subset.matrix, diag = T)] <- NA
redundant <- colSums(subset.matrix, na.rm = T) >= 1

# Output plot
plot(rules, method = "graph", engine = "htmlwidget")

2.2.4 Cluster Analysis K-Means

K-Means is a clustering method in which the datasets are divided into a series of k groups, where k is the number of groups specified by the analyst.

The following R codes show how to determine the optimal number of clusters and how to compute K-Means and PAM clustering in R.

Determining the optimal number of clusters:

# Loading libraries
library(cluster)
library(factoextra)
library(pheatmap)

# Creating dataset of crime in the USA
mydata <- scale(USArrests) 

# K-Means Clustering
fviz_nbclust(mydata, kmeans, method = "gap_stat")
Fig. 2.2.4a: Optimal Number of Clusters

Fig. 2.2.4a: Optimal Number of Clusters

Computing and visualizing the K-Means Cluster:

set.seed(123) # for reproducibility
km.res <- kmeans(mydata, 3, nstart = 25)

# Visualizing K-Means clusters
fviz_cluster(km.res, data = mydata, palette = "jco", ggtheme = theme_minimal(), barfill = "red", barcolor   = "red", linecolor = "red")
Fig. 2.2.4b: Cluster

Fig. 2.2.4b: Cluster

Hierarchical clustering is an alternative approach to partitioning clustering to identify groups in a dataset. In this method, the number of clusters to be generated does not need to be specified in advance.

The result of hierarchical clustering is a tree-like representation of the objects, which is also called a dendrogram. Observations can be divided into groups by cutting the dendrogram at a desired similarity level:

# Hierarchical clustering
# Cluster dendrogram
res.hc <- hclust(dist(mydata),  method = "ward.D2")
fviz_dend(res.hc, cex = 0.5, k = 4, palette = "jco")
Fig. 2.2.4c: Cluster Dendrogram

Fig. 2.2.4c: Cluster Dendrogram

A heatmap is another way to visualize hierarchical clustering. It is also called a false color image, where data values are converted to a color scale. With heatmaps, we can simultaneously visualize groups of samples and features:

# Creating heatmap
pheatmap(t(mydata), cutree_cols = 4)
Fig. 2.2.4d: Cluster Heatmap

Fig. 2.2.4d: Cluster Heatmap

2.2.5 Neuronale Netze-Analyse

A neural network is an information processing machine and can be considered an analog to the human nervous system. Just like the human nervous system, which consists of interconnected neurons, a neural network is composed of interconnected information processing units. The information processing units do not work in a linear way. Rather, the neural network derives its strength from the parallel processing of information, which enables it to deal with nonlinearity. Neural networks are useful for deriving meaning from complex datasets and recognizing patterns.

Here the neural network is visualized. Our model has 3 neurons in its hidden layer. The black lines show the connections with the weights. The weights are calculated using the backpropagation algorithm explained earlier. The yellow lines represent the bias term:

# Loading 'neuralnet' library
library(neuralnet)

# Reading data
data <- read.csv("cereals.csv", header=T)

# Random sampling
samplesize = 0.60 * nrow(data)
set.seed(80)
index <- sample( seq_len ( nrow ( data ) ), size = samplesize )

# Creating training and test datasets
datatrain <- data[ index, ]
datatest <- data[ -index, ]

# Scaling data for neural network
max <- apply(data , 2 , max)
min <- apply(data, 2 , min)
scaled <- as.data.frame(scale(data, center = min, scale = max - min))

## Fitting neural network
# Creating training and test datasets
trainNN <- scaled[index , ]
testNN <- scaled[-index , ]

# Fitting neural network
set.seed(2)
NN <- neuralnet(rating ~ calories + protein + fat + sodium + fiber, trainNN, hidden = 3 , linear.output = T )

# Creating plot
plot(NN)
Fig. 2.2.5a: Neural Network

Fig. 2.2.5a: Neural Network

Here the model rating is predicted using the neural network model. The predicted rating can be compared with the real rating through visualization. The RMSE for the neural network model is 6.05:

## Prediction using the neural network
predict_testNN <- compute(NN, testNN[,c(1:5)])
predict_testNN <- (predict_testNN$net.result * (max(data$rating) - min(data$rating))) + min(data$rating)

# Creating plot and regression line
plot(datatest$rating, predict_testNN, col='blue', pch=16, ylab = "predicted rating NN", xlab = "real rating")
abline(0,1)
Fig. 2.2.5b: Neural Network

Fig. 2.2.5b: Neural Network

2.3 Miscellaneous misc

Here you will find code examples, fun stuff and news about technical applications & data analysis:

2.3.1 Example R Code

This example shows the use of loops in R. Loops are frequently used in programming, e.g. to check matches in two different datasets.

# Komplexere R Skript (Programmierung)

# Einfacher Vektor, die Funktion c kombiniert Werte in einen Vektor oder eine Liste
fruitVec <- c("Apfel", "Banane", "Orange", "Birne") # fruitVec wird mit 4 Werten (Strings) gefüllt

# Einfache While-Schleife
# Funktion length: gibt die Länge eines/r Vektors / Liste aus
# Der Vektor fruitVec kann wie ein Array angesprochen werden, um die einzelnen Werte auszulesen
pos <- 1
while (pos <= length(fruitVec)) {
  print(paste0("Die Frucht Nr.", pos, " ist : ", fruitVec[pos]))
  pos <- pos + 1
}
[1] "Die Frucht Nr.1 ist : Apfel"
[1] "Die Frucht Nr.2 ist : Banane"
[1] "Die Frucht Nr.3 ist : Orange"
[1] "Die Frucht Nr.4 ist : Birne"
# Einfache For-Schleife
# Funktion paste0 verbindet Strings
# Funktion which ermittelt die Position eines Wertes im Vektor (bzw. Array)
help(which)
for (fruit in fruitVec) {
  print(paste0("Die Frucht Nr.", which(fruit == fruitVec), " ist: ", fruit))
}
[1] "Die Frucht Nr.1 ist: Apfel"
[1] "Die Frucht Nr.2 ist: Banane"
[1] "Die Frucht Nr.3 ist: Orange"
[1] "Die Frucht Nr.4 ist: Birne"

2.3.2 Execute External R Code

This code is in the file example.R and is read and executed by R Markdown.

# x Werte von 1 und 100 zuweisen
x <- 1:100
# y 100 Werte zuweisen mit x + Zufallszahl (-5 bis +5)
y <- x + rnorm(100, sd = 5)
# Gibt den ersten oder letzten Teil eines Vektors, einer Matrix oder einer Tabelle zurück
head(data.frame(x, y))
plot(x, y)
Error : The fig.showtext code chunk option must be TRUE

2.3.3 Cat Statistics

1000 scientists have found out completely independently from each other (in compliance with all scientific requirements):

Fig. 2.3.7a: Cat Statistics

Fig. 2.3.7a: Cat Statistics

2.3.4 Big Data Jobs

An interesting article (if no longer available - click on the article) that identifies jobs in the Big Data field and lists possible salaries (in dollars):

PDF Loading Page Top 7 Big Data Jobs

2.3.5 Serious Ben Entertainment

Here is my Serious Ben Entertainment website for eHealth services which I created during my studies at University of Edinburgh in the Data Science for Health and Social Care (M. Sc.) program:

Serious Ben Entertainment Landing Page Serious Ben Entertainment Landing Page

References lit.

Here is the literature used in Data Science courses:

  • Cleve, J/Lämmel, U. [2020]
    Data Mining, 3. Auflage, Berlin/Boston 2020

  • Romeijn, J. W. [2016]
    Philosophy of Statistics. In E. N. Zalta (Hrsg.), The Stanford Encyclopedia of Philosophy, Stanford 2016

  • Sauer, S. [2019]
    Moderne Datenanalyse mit R, Wiesbaden 2019

  • Tukey, J. W. [1962]
    The future of data analysis. The Annals of Mathematical Statistics, Vol. 33, No. 1, Institute of Mathematical Statistics 1962

  • Wickham, H./Garrett G. [2017]
    R for Data Science, O‘Reilly Media 2017

  • Wozabal, D. [2007]
    Statistisches Programmieren – Regressionen in R (Session 6), 2007

  1. Sauer [2019]↩︎

  2. Wozabal [2007]↩︎

Benjamin Groß, Subbelratherstr. 337, 50825 Cologne, Germany.

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