Notifications
Exam terms: Fri Jan 13, Wed Jan 18, Fri Jan 20, Mon Jan 23, Fri Jan 27, Wed Feb 1, Fri Feb. 3. Capacity: 12 students each. Schedule: morning 8:30-10:00 written part, afternoon 12:00-?? oral part.
There will be no exam terms in the week Feb. 6-Feb 10. One additional term may be made available during the first three weeks of the summer semester.
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.
- Course notes for 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.
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.
Detailed Course Syllabus
- Introduction
- Simple linear regression: technical and historical
view
Lecture 1, Sep. 30 - 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 - Properties of LS estimates
- Moment properties
Lecture 6, Oct. 18 - Gauss-Markov theorem
Lecture 6, Oct. 18 - Properties under normality
Lecture 6, Oct. 18 - 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 - 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 - 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 - Transformation of the response
- Interpretation of log-transformed model
Lecture 12, Nov. 11 - Box-Cox transformation
Lecture 12, Nov. 11 - 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 - 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
Lecture 17, Nov. 29 - Confidence band for the whole regression surface
Lecture 17, Nov. 29 - Interactions
- Interactions of two factors: two-way ANOVA
Lecture 18, Dec. 2 - Interactions of two numerical covariates
Lecture 18, Dec. 2 - Interactions of a numerical covariate with a factor
Lecture 18, Dec. 2 - Regression model with multiple covariates
- Decomposition of the model with additional covariate
Lecture 19, Dec. 6 - Effects on fitted values, residuals, SSe, parameter estimates,
predictions
Lecture 19, Dec. 6 - Orthogonal covariates
Lecture 20, Dec. 9 - Decomposition of regression sum of squares
- Multicollinearity, variance inflation factor
Lecture 20, Dec. 9 - Confounding bias, mediation, assessment of causality
Lecture 21, Dec. 13 - Analysis of variance (ANOVA) models
- One-way ANOVA review
Lecture 22, Dec. 16 - Two-way ANOVA with/without interactions
Lecture 22, Dec. 16 - Balanced two-way ANOVA
- Nested factor effects
- Dealing with heteroskedasticity
- Weighted least squares
- White's sandwich estimator
- Covariate measurement errors
- Missing data issues in regression models
- 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
- Model Checking and Diagnostic Methods II.
- Independence of error terms
- Leverage points, outliers
- Influential observations
- Jackknife residuals
- DFBetas
- Cook's distance