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Notifications

Complete hand-written lecture 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).

Exam terms: Fri Jan 17, Tue Jan 21, Fri Jan 24, Tue Jan 28 (afternoon), Thu Feb 6, Thu Feb 13. Capacity of each term: 10 students. Schedule (except Jan. 28): 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.

Schedule 

Lectures
Monday 14:00 - 15:30 K1  
Friday 11:30 - 13:00 K2  
Tutorial Classes (Link to Moodle)
Thursday 15:40 - 17:10 K4 Instructor: Marek Omelka

Course Materials 

Lecture notes covering the first 6 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.

Progress of Lectures  

  1. Introduction
    • Simple linear regression: technical and historical review
      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 2, Oct. 4
    • Geometric interpretation of LSE
      Lecture 3, Oct. 7
    • Equivalence of LR models
      Lecture 3, Oct. 7
    • Model with centered covariates
      Lecture 3, Oct. 7
    • Decomposition of sums of squares, coefficient of determination
      Lecture 4, Oct. 11
    • LSE under linear restrictions
      Lecture 4 and 5, Oct. 11 and 14
  3. Properties of LS estimates
    • Moment properties
      Lecture 5, Oct. 14
    • Gauss-Markov theorem
      Lecture 5, Oct. 14
    • Properties under normality
      Lecture 6, Oct. 18
  4. Statistical inference in LR model
    • Exact inference under normality
      Lecture 6, Oct. 18
    • Submodel testing
      Lecture 6 and 7, Oct. 18 and 21
    • One-way ANOVA model
      Lecture 7, Oct. 21
    • Connections to maximum likelihood theory
      Lecture 7, Oct. 21
    • Asymptotic inference with random covariates
      Lecture 8, Oct. 25
    • Asymptotic inference with fixed covariates
      Lecture 9, Nov. 1
  5. Predictions
    • Confidence interval for estimated conditional mean of an existing/future observation
      Lecture 9, Nov. 1
    • Confidence interval for the response of a future observation
      Lecture 9, Nov. 1
  6. Model Checking and Diagnostic Methods I.
    • Residuals, standardized residuals
      Lecture 9, Nov. 1
    • Residual plots, QQ plots
      Lecture 10, Nov. 4
  7. Transformation of the response
    • Interpretation of log-transformed model
      Lecture 10, Nov. 4
    • Box-Cox transformation
      Lecture 10, Nov. 4
  8. Parametrization of a single covariate
    • Single categorical covariate (one-way ANOVA model)
      Lecture 11, Nov. 8
    • Single numerical covariate
      Lecture 12-13, Nov. 11 and 15
  9. Multiple tests and simultaneous confidence intervals
    • Bonferroni method
      Lecture 13, Nov. 15
    • Tukey method
      Lecture 14, Nov. 18
    • Scheffé method
      Lecture 15, Nov. 22
    • Confidence band for the whole regression surface
      Lecture 15, Nov. 22
  10. Interactions
    • Interactions of two factors: two-way ANOVA
      Lecture 16, Nov. 25
    • Interactions of two numerical covariates
      Lecture 16, Nov. 25
    • Interactions of a numerical covariate with a factor
      Lecture 17, Nov. 29
  11. Analysis of variance (ANOVA) models
    • One-way ANOVA review
      Lecture 17, Nov. 29
    • Two-way ANOVA with/without interactions
      Lecture 17 and 18, Nov. 29 and Dec. 2
    • Balanced two-way ANOVA
      • Lecture 18, Dec. 2
    • Nested factor effects
      • Lecture 19, Dec. 6
  12. Regression model with multiple covariates
    • Model with additional covariates: fitted values, residuals, SSe, parameter estimates, predictions
      Lecture 19 and 20, Dec. 6 and 9
    • Orthogonal covariates
      Lecture 20, Dec. 9
    • Multicollinearity, variance inflation factor
      Lecture 21, Dec. 13
    • Confounding bias, mediation, assessment of causality
      Lecture 21, Dec. 13
  13. Heteroskedasticity
    • Weighted least squares
      Lecture 22, Dec. 16
    • White's sandwich estimator
      Lecture 22, Dec. 16
  14. Sources of bias
    • Covariate measurement errors
      Lecture 23, Jan. 6
    • Sampling bias, missing data
      Lecture 23, Jan. 6
 

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 tutorial credit is required to register for the 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.