To introduce linear statistical models and their applications in estimation and testing. The course will illustrate concepts with specific examples, data sets and numerical exercises using statistical package R.

Lectures-Tutorials-Practicals-Credits: 4-0-0-4

Week 1: Basic statistics; Introduction to R; Data visualization using ggplot2 and geoms.

Week 2: Introduction to linear models; Residual analysis; Working with datasets in R.

Week 3: Fundamentals of linear models; Parameter estimation problem; Theory of linear regression.

Week 4: Classification of linear models; Least squares estimation; Normal equations; Matrix fundamentals.

Week 5: Estimation of regression coefficients; Hypothesis testing and confidence intervals; Model evaluation (RSE, R²); Implementation in R.

Week 6: Gauss-Markov theorem; BLUE (best linear unbiased estimator); Variance analysis; Normality assumptions.

Week 7: Applications of Gauss-Markov theorem; Multiple regression visualization; Real data analysis and simulations in R.

Week 8: Hypothesis testing in regression; Testing linear hypotheses; ANOVA concepts; Least squares theory extensions.

Week 9: One-way and two-way classification models; ANOVA testing; Model evaluation in general cases.

Week 10: Statistical testing in R; t-tests for simple and multiple regression; One-way ANOVA implementation.

Week 11: Random effects models; One-way and two-way random effects; Mixed effects models; ANOVA using R.

Week 12: Fixed vs random effects models; Implementation in R; Model comparison and interpretation.