Notifications
Course materials have been updated on Jan. 12. Look here.
Exam terms: Fri Jan 19, Wed Jan 24, Fri Jan 26, Fri Feb 2, Mon Feb 5, Fri Feb. 9. Capacity of each term: 10 students. Schedule: morning 9:00-10:30 written part, afternoon from cca 12:30 oral part.
Getting a tutorial credit is required for exam registration.
Click here to see how the exam is organized.
If you need individual arrangements or modifications in the exam/exam schedule for an objective reason (special needs but not only that) or if you get in trouble with scheduling your exams for reasons that are out of your control, contact me by email.
There will be no exam terms in the week Feb. 12-Feb 16. One additional term with a limited capacity may be made available during the first three weeks of the summer semester if the capacity of the last exam term(s) is exhausted.
Schedule
| Lectures | |||
| Tuesday | 15:40 - 17:10 | K2 | |
| Friday | 10:40 - 12:10 | K1 | |
| Tutorial Classes (Link to Moodle) | |||
| Monday | 9:00 - 10:30 | K4 | Instructor: Šárka Hudecová |
| Friday | 12:20 - 13:50 | K11 | Instructor: Marek Omelka |
Course Materials
Lecture notes covering the first 3 chapters of the lecture are available below. Complete hand-written notes can be downloaded from the course webpage in the SIS (only accessible by the students who are registered for the course, requires log-in). Another link below downloads old regression lecture notes authored by Arnošt Komárek. Almost all the topics are covered there, although in a different order and a different level of detail. The last link is a textbook that can be used as a complementary resource.
- Unfinished lecture notes.
- A slideshow of pictures used in the lectures this year.
- Lecture notes from 2021/22 by Arnošt Komárek
-
Yan, X. and Su, X. (2009)
Linear Regression Analysis: Theory And Computing. Singapore: World Scientific. 2009. Available to students of Charles Univeristy as an online e-book.
Progress of Lectures
- Introduction
- Simple linear regression: technical and historical
review
Lecture 1, Oct. 3 - Linear regression model
- Definition, assumptions
Lecture 1, Oct. 3 - Interpretation of regression parameters
Lecture 2, Oct. 6 - Least squares estimation (LSE)
Lecture 2 , Oct. 6 - Residual sums of squares, fitted values, hat matrix
Lecture 3, Oct. 6 - Geometric interpretation of LSE
Lecture 3, Oct. 10 - Equivalence of LR models
Lecture 3, Oct. 10 - Model with centered covariates
Lecture 3-4, Oct. 10 and 13 - Decomposition of sums of squares, coefficient of determination
Lecture 4, Oct. 13 - LSE under linear restrictions
Lecture 5, Oct. 17 - Properties of LS estimates
- Moment properties
Lecture 5, Oct. 17 - Gauss-Markov theorem
Lecture 6, Oct. 20 - Properties under normality
Lecture 6, Oct. 20 - Statistical inference in LR model
- Exact inference under normality
Lecture 6-7, Oct. 20 and 24 - Submodel testing
Lecture 7, Oct. 24 - One-way ANOVA model
Lecture 8, Oct. 27 - Connections to maximum likelihood theory
Lecture 8, Oct. 27 - Asymptotic inference with random covariates
Lecture 8-9, Oct. 27 and 31 - Asymptotic inference with fixed covariates
Lecture 9, Oct. 31 - Predictions
- Confidence interval for estimated conditional mean of an existing/future observation
Lecture 10, Nov. 3 - Confidence interval for the response of a future observation
Lecture 10, Nov. 3 - Model Checking and Diagnostic Methods I.
- Residuals, standardized residuals
Lecture 10, Nov. 3 - Residual plots, QQ plots
Lecture 10-11, Nov. 3 and 7 - Transformation of the response
- Interpretation of log-transformed model
Lecture 11, Nov. 7 - Box-Cox transformation
Lecture 12, Nov. 10 - Parametrization of a single covariate
- Single categorical covariate (one-way ANOVA model)
Lecture 12, Nov. 10 - Single numerical covariate
Lecture 13-14, Nov. 14 and 21 - Multiple tests and simultaneous confidence intervals
- Bonferroni method
Lecture 15, Nov. 24 - Tukey method
Lecture 16, Nov. 28 - Scheffé method
Lecture 16-17, Dec. 1 - Confidence band for the whole regression surface
Lecture 17, Dec. 1 - Interactions
- Interactions of two factors: two-way ANOVA
Lecture 17, Dec. 1 - Interactions of two numerical covariates
Lecture 18, Dec. 5 - Interactions of a numerical covariate with a factor
Lecture 18, Dec. 5 - Analysis of variance (ANOVA) models
- One-way ANOVA review
Lecture 18, Dec. 5 - Two-way ANOVA with/without interactions
Lecture 18-19, Dec. 5 and 8 - Balanced two-way ANOVA Lecture 19, Dec. 8
- Nested factor effects Lecture 20, Dec. 12
- Regression model with multiple covariates
- Model with additional covariates: fitted values, residuals, SSe,
parameter estimates, predictions
Lecture 21, Dec. 15 - Orthogonal covariates
Lecture 22, Dec. 19 - Multicollinearity, variance inflation factor
Lecture 22, Dec. 19 - Confounding bias, mediation, assessment of causality
Lecture 22-23, Dec. 19 and Jan. 5 - Heteroskedasticity
- Weighted least squares
Lecture 23, Jan. 5 - White's sandwich estimator
Lecture 23-24, Jan. 5 and 9 - Sources of bias
- Covariate measurement errors
Lecture 24-25, Jan. 9 and 12 - Sampling bias, missing data
Lecture 25, Jan. 12
Requirements for Credit/Exam
Tutorial Credit:
The credit for the tutorial sessions will be awarded to the student who satisfies the following two conditions:
- 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.
- 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.
The written part includes five questions. The first question is elementary and must be answered correctly in order to pass the exam. The other four questions are worth 5 points each and cover the folowing topics: Basic properties of the LSE, Statistical inference in the LR model, Interpretation of regression parameters, Asymptotics in LR model, Weighted Least Squares. You must get at least 11 points from these 4 questions (in addition to the compulsory 1st question). The time limit is 90 minutes.
If you pass the written part you can proceed to the oral part. You will get one question that combines topics taken from the whole lecture contents. You are expected to put together a coherent presentation of the assigned topic (introduce the notation, define relevant terms, present important theorems with proofs and derivations of important results). You are supposed to demonstrate understanding of your topic, not just ability to literally reproduce parts of the lecture. There is no time limit for the oral part.
The exam grade is a combined evaluation of your performance at the written and oral parts.