Each module contains 3 ECTS. You choose a total of 10 modules/30 ECTS in the following module categories:

- 12-15 ECTS in technical scientific modules (TSM)

TSM modules teach profile-specific specialist skills and supplement the decentralised specialisation modules. - 9-12 ECTS in fundamental theoretical principles modules (FTP)

FTP modules deal with theoretical fundamentals such as higher mathematics, physics, information theory, chemistry, etc. They will teach more detailed, abstract scientific knowledge and help you to bridge the gap between abstraction and application that is so important for innovation. - 6-9 ECTS in context modules (CM)

CM modules will impart additional skills in areas such as technology management, business administration, communication, project management, patent law, contract law, etc.

In the module description (download pdf) you find the entire language information per module divided into the following categories:

- instruction
- documentation
- examination

This course will provide an introductory review of the basic concepts of probability and statistics to understand probability distributions and to produce rigorous statistical analysis including estimation, hypothesis testing, and confidence intervals. Students will be introduced to the basic concepts of predictive modelling which by definition is the analysis of current and historical facts to make predictions about future events. Students will learn several techniques that account for many business and engineering applications of predictive modelling. These include regression techniques, time series models, and classification methods. Applicability and limitations of these methods will be illustrated in the light of data sets and analyses using the statistical software R.

### Prerequisites

Basic knowledge of statistics on the level of an introductory stochastics course. Linear algebra: matrix-vector calculations. Basic Calculus.

Familiarity and experience with programming, in particular with scripting languages like Matlab, Python or R. We will provide the students with a self-test to assess their prior knowledge in statistics and scripting.

### Learning Objectives

Students are able to analyze data by means of regression analysis. They are familiar with important statistical forecasting methods and are able to calculate, evaluate and interpret predictions. They are able to choose an appropriate statistical method for a regression, classification or time series problem. They are able to evaluate and compare statistical models.

### Contents of Module

*Fundamental concepts of probability and statistics (repetition of basic courses):* concept of random variable, important probability distributions, covariance, parameter estimation, hypothesis testing, and confidence intervals.

*Regression analysis:* Simple linear regression with parameter estimation, graphical model validation, transformation of variables, confidence and prediction intervals for parameters. Multiple linear regression with parameter estimation, statistical tests and confidence intervals for parameters, and variable selection.

*Classification:* Concepts of classification, logistic regression, CART, random forests and model evaluation by cross-validation.

*Time series analysis:* STL decomposition, confidence and prediction bands, AR models with parameter estimation, confidence and prediction bands, autocorrelation, and model selection.

### Teaching and Learning Methods

Lecture and practical work on computer with the statistics software R.

### Literature

Lecture notes will be available in addition to recommended book chapters.

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