# Teaching

## M 305 Statistics

Semester:
Aims and objectives:

To provide an introduction to statistical inference, namely estimation and hypothesis testing. Based on the foundations of inference, the objective is to discuss the theory of linear models, especially the linear regression model and its related topics. If time permits, analyze some real data using statistical software R.

Syllabus:

Introduction: population, sample, parameters; point estimation: properties of estimators: unbiasedness, mean square error and relative efficiency, consistency; methods ofestimation: method of moments, maximum likelihood estimation and its properties;Bayes and minimax estimation; confidence interval estimation: mean, variance for bothnormal and non-normal cases, proportions, difference of means, bootstrap confidenceinterval, test of Hypothesis: simple and composite hypotheses; Type I and Type II errors, power, Neyman-Pearson lemma, examples of MP and UMP tests: normal mean,variance, proportions, two sample tests, p-values, sample size and power calculations,likelihood ratio tests for composite hypotheses; Bayes and minimax procedures; introduction to statistical modeling: scatter diagram, sample correlation, simple linearregression, least squares estimation and testing concerning the parameters of regressionmodel, prediction problem, graphical residual analysis, Q-Q plot to test normality ofresiduals, multiple regression, analysis of variance, analysis of categorical data: contingency tables and chi-square tests.

Mode of evaluation:
Absolute
Important dates:

To be announced later