Schedule

 Lectures Tuesday 15:40 - 17:10 K3 Friday 13:10 - 14:40 K2 Tutorial Classes (Link to Moodle) Wednesday 9:00 - 10:30 K11 Instructor: Šárka Hudecová Wednesday 10:40 - 12:10 K11 Instructor: Marek Omelka

Course Materials

The course contents has been revamped since its previous form (2021 and earlier). Hence, no course notes adapted to the current syllabus will be available this year. Students can use the link below to download the course notes from the previous year. Almost all the topics are covered there, although in a different order and a different level of detail.

Requirements for Credit/Exam

Tutorial Credit:

The credit for the tutorial sessions will be awarded to the student who satisfies the following two conditions:

1. Regular small assignments: A student needs to prepare acceptable solutions to at least 10 out of 12 tutorial class assignments. An assignment can be solved either during the corresponding tutorial class or the solution needs to be submitted within a pre-specified deadline.
2. Project: A student needs to submit a project satisfying the requirements given in the assignment. A corrected version of an unsatisfactory project can be resubmitted once.

The nature of these requirements precludes any possibility of additional attempts to obtain the tutorial credit (with the exceptions listed above).

Exam:

The exam has two parts: written and oral, both conducted on the same day.

Detailed Course Syllabus

1. Introduction
• Simple linear regression: technical and historical view
Lecture 1, Sep. 30
2. Linear regression model
• Definition, assumptions
Lecture 1, Sep. 30
• Interpretation of regression parameters
Lecture 2, Oct. 4
• Least squares estimation (LSE)
Lecture 2 , Oct. 4
• Residual sums of squares, fitted values, hat matrix
Lecture 3, Oct. 7
• Geometric interpretation of LSE
Lecture 3, Oct. 7
• Equivalence of LR models
Lecture 3, Oct. 7
• Model with centered covariates
Lecture 4, Oct. 11
• Decomposition of sums of squares, coefficient of determination
Lecture 4-5, Oct. 11 and 14
• LSE under linear restrictions
Lecture 5, Oct. 14
3. Properties of LS estimates
• Moment properties
Lecture 6, Oct. 18
• Gauss-Markov theorem
Lecture 6, Oct. 18
• Properties under normality
Lecture 6, Oct. 18
4. Statistical inference in LR model
• Exact inference under normality
Lecture 7, Oct. 21
• Submodel testing
Lecture 8, Oct. 25
• One-way ANOVA model
Lecture 8, Oct. 25
• Connections to maximum likelihood theory
Lecture 9, Nov. 1
• Asymptotic inference with random covariates
Lecture 9-10, Nov. 1 and 4
• Asymptotic inference with fixed covariates
Lecture 10, Nov. 4
5. Predictions
• Possible objectives or regression analysis.
Lecture 10, Nov. 4
• Pitfalls of predictions
Lecture 10, Nov. 4
• Confidence interval for estimated conditional mean of an existing/future observation
Lecture 10, Nov. 4
• Confidence interval for the response of a future observation
Lecture 11, Nov. 8
6. Model Checking and Diagnostic Methods I.
• Residuals, standardized/studentized residuals
Lecture 11, Nov. 8
• Residual plots, QQ plots
Lecture 11, Nov. 8
• Checking homoskedasticity
Lecture 11, Nov. 8
7. Transformation of the response
• Interpretation of log-transformed model
Lecture 12, Nov. 11
• Box-Cox transformation
Lecture 12, Nov. 11
8. Parametrization of a single covariate
• Single factor covariate (one-way ANOVA model)
Lecture 12-13, Nov. 11 and 15
• Single numerical covariate
Lecture 14-15, Nov. 18 and 22
9. Multiple tests and simultaneous confidence intervals
• Bonferroni method
Lecture 15-16, Nov. 22 and 25
• Tukey method
Lecture 16-17, Nov. 25 and 29
• Scheffé method
• Confidence band for the whole regression surface
10. Interactions
• Interactions of two factors: two-way ANOVA
• Interactions of two numerical covariates
• Interactions of a numerical covariate with a factor
11. Regression model with multiple covariates
• Decomposition of the model with additional covariate
• Effects on fitted values, residuals, RSS, coef. of determination
• Effects on parameter estimates
• Orthogonal covariates
• Decomposition of regression sum of squares
• Multicollinearity
• Confounding bias
• Mediation
• Assessment of causality
12. Analysis of variance (ANOVA) models
• One-way ANOVA
• Two-way ANOVA without interactions
• Two-way ANOVA with interactions
13. Model-building strategies
• Model choice based on sequential submodel testing
• Functional form of numerical covariates
• Inclusion of interactions
• Goodness of fit measures
• Step-wise procedures
• Comparison to AI methods
14. Model Checking and Diagnostic Methods II.
• Independence of error terms
• Leverage points, outliers
• Influential observations
• Jackknife residuals
• DFBetas
• Cook's distance
15. Weighted least squares
16. Dealing with heteroskedasticity: sandwich estimation
• Linear model without equal variance assumption - asymptotics
• White estimator
17. Covariate measurement errors
18. Missing data issues in regression models