Course syllabus for Linear statistical models

Course syllabus adopted 2021-02-26 by Head of Programme (or corresponding).

Overview

  • Swedish nameLinjära statistiska modeller
  • CodeMVE190
  • Credits7.5 Credits
  • OwnerMPENM
  • Education cycleSecond-cycle
  • Main field of studyMathematics
  • DepartmentMATHEMATICAL SCIENCES
  • GradingTH - Pass with distinction (5), Pass with credit (4), Pass (3), Fail

Course round 1

  • Teaching language English
  • Application code 20133
  • Maximum participants100 (at least 10% of the seats are reserved for exchange students)
  • Open for exchange studentsYes

Credit distribution

0108 Examination 7.5 c
Grading: TH		 7.5 c
  • 14 Jan 2025 pm J
  • 15 Apr 2025 pm J

In programmes

Examiner

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Eligibility

General entry requirements for Master's level (second cycle)
Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling the requirements above.

Specific entry requirements

English 6 (or by other approved means with the equivalent proficiency level)
Applicants enrolled in a programme at Chalmers where the course is included in the study programme are exempted from fulfilling the requirements above.

Course specific prerequisites

MVE155 Statistical inference or a similar course

Aim

Understand the common mathematical structure of linear regression models and generalised linear models; construct and use these models for data analysis using statistical inference and suitable software; interpret the results and criticise the model limitations.

Learning outcomes (after completion of the course the student should be able to)

  • explain the common mathematical structure of linear regression models and generalized linear models 
  • construct and use these models for data analysis using statistical inference and suitable software 
  • interpret the results and criticize the model limitations 
  • identify data analysis situations for which linear models apply naturally and to estimate and interpret parameters
  • predict future observations and test hypotheses using suitable software such as R 
  • construct regression models that are suitable for the current data but can also generalize to future observations 
  • explain the model limitations, identify situations where the hypothesized model is not suitable for the given data, and possibly transform the data to increase the model predictive ability

Content

  • simple linear and multivariate linear models and underlying assumptions
  • the bias/variance trade-of
  • properties of least squares estimators
  • identification of outliers and the use of residuals and other diagnostics to verify if model assumptions are met;
  • the use of categorical covariates in regression.
  • testing parameters using the t-test;
  • goodness of fit indices (R2 and adjusted R2).
  • confidence and prediction intervals.
  • the multicollinearity problem, its identification and remedial measures.
  • Model selection via greedy algorithms (stepwise procedures) and the AIC.
  • Model selection via the partial F test;
  • Prediction error and cross validation.
  • Interaction between covariates.
  • an introduction to generalised linear models, the exponential family, and asymptotic properties of the maximum likelihood estimators.
  • testing procedures for generalised linear models.

Organisation

Lectures; weekly (or almost weekly) mini-projects and presentations

Literature

Updated on a yearly basis - please check course homepage

Examination including compulsory elements

Summary report of the weekly mini-projects; a final project report; a written exam. Attendance to the weekly presentations of mini-analyses is mandatory. See the course page for how to compensate for missed attendance.

The course examiner may assess individual students in other ways than what is stated above if there are special reasons for doing so, for example if a student has a decision from Chalmers on educational support due to disability.