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 ebook.
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 prespecified 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 45, Oct. 11 and 14  LSE under linear restrictions
Lecture 5, Oct. 14  Properties of LS estimates
 Moment properties
Lecture 6, Oct. 18  GaussMarkov 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  Oneway ANOVA model
Lecture 8, Oct. 25  Connections to maximum likelihood theory
Lecture 9, Nov. 1  Asymptotic inference with random covariates
Lecture 910, 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 logtransformed model
Lecture 12, Nov. 11  BoxCox transformation
Lecture 12, Nov. 11  Parametrization of a single covariate
 Single factor covariate (oneway ANOVA model)
Lecture 1213, Nov. 11 and 15  Single numerical covariate
Lecture 1415, Nov. 18 and 22  Multiple tests and simultaneous confidence intervals
 Bonferroni method
Lecture 1516, Nov. 22 and 25  Tukey method
Lecture 1617, Nov. 25 and 29  Scheffé method
 Confidence band for the whole regression surface
 Interactions
 Interactions of two factors: twoway ANOVA
 Interactions of two numerical covariates
 Interactions of a numerical covariate with a factor
 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
 Analysis of variance (ANOVA) models
 Oneway ANOVA
 Twoway ANOVA without interactions
 Twoway ANOVA with interactions
 Modelbuilding strategies
 Model choice based on sequential submodel testing
 Functional form of numerical covariates
 Inclusion of interactions
 Goodness of fit measures
 Stepwise 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
 Weighted least squares
 Dealing with heteroskedasticity: sandwich estimation
 Linear model without equal variance assumption  asymptotics
 White estimator
 Covariate measurement errors
 Missing data issues in regression models