- Thesis:
- Bachelor in Mathematics 50%
- Author:
- Melissa Weber
- Title:
- Lineare Einfachregression insbesondere in höherdimensionalen Modellen
- Supervisors:
- Sergio Brenner Miguel
- Jan JOHANNES
- Abstract:
- In the following elaboration, the linear simple regression is introduced and extended with input data of higher dimension. The focus will be on the distinction between deterministic and stochastic input data. That means the first two chapters are considered separately for fixed and random data, so that the respective advantages and also limitations are clearly expressed. A large chapter deals with the possibility to determine the estimators in a (multiple) linear regression using the least squares method and concludes with theoretical results such as the Gauß-Markov theorem, which shows that the least squares estimator is the best linear unbiased estimator. This chapter can be applied to all dimensions of input data and divides into fixed and random design only for certain inferences. Finally, ridge regression is introduced with focus on graphical visualization as well as implementation in the statistical software R. This regression is interesting as it shows some advantages over least squares estimator especially in high dimensions. An outlook at the end of the paper is intended to stimulate further interest in the topic and to give an idea for its possible continuation.
- References:
- S. Richter. Statistisches und maschinelles Lernen, Springer Spektrum, Berlin, 2019.
| Statistics Group | Institute for Mathematics | Faculty of Mathematics and Computer Science | University Heidelberg |