Linear Models

LMAC MECD MMAC

Class notes

  1. Linear models

    1.1 Introduction

    1.2 The simple linear regression model – a review ([K] Ch. 1, § 2.1 – § 2.5, § 2.9)

    1.3 The general linear model

  2. Linear regression model

    2.1 The multiple linear regression model ([K] § 6.1, § 6.2)

    2.2 Estimation and prediction ([K] § 6.3, § 6.4, § 6.6, § 6.7)

    2.3 Tests for regression coefficients ([K] § 6.5, § 7.1 – § 7.4)

    2.4 Categorical covariates ([K] § 8.3 – § 8.7)

  3. Building the regression model

    3.1 Diagnostics and corretive measures ([K] § 6.8, Ch. 10 and 11)

    3.2 Selection of variables ([K] § 9.3 – 9.5)

    3.3 Model validation ([K] § 9.6)

  4. Analysis of variance (ANOVA)

    4.1 Single-factor ANOVA ([K] § 16.3 – 16.8)

    4.2 Two-factor ANOVA ([K] § 19.3, 19.8, 19.9)

  5. Other models

    5.1 Penalized regression

    5.2 Generalized linear models

  1. Matrix algebra and some distributions ([K] § 5.1 – § 5.8, [S])

Books and stuff

Main reference

  1. Kutner, M. H., Nachtsheim, C. J., Neter, J. & Li, W. (2005). Applied linear statistical models, 5th edition. McGraw-Hill/Irwin. [K]

Complementary references

  1. Faraway, J. J. (2014). Linear Models with R, 2nd edition. Chapman and Hall/CRC. [F]

  2. Searle, S. R. & Khuri, A. I. (2017). Matrix algebra useful for statistics. John Wiley & Sons. [S]

Software

Assignments

Lab#1 (September 26, 2025) – Simple linear regression model

Lab#2 (October 10, 2025) – Multiple linear regression model 1

Project assignment (November, 10, 2025)

Lab#3 (November 14, 2025) – Multiple linear regression model 2

Lab#4 (November 21, 2025) – Diagnostics and model selection

Lab#5 (December 5, 2025) – ANOVA models

Lab#6 (December 17, 2025) – Penalized regression

Lab#7 (December 19, 2025) – Generalized linear models

Past test

Current semester

First test (17/10/2025)

2024/2025

Second exam (06/02/2025)

First exam (23/01/2025)

2023/2024

Second exam (31/01/2024)

First exam (17/01/2024)

About

What is this?

This is a set of notes written for a one semester course on Linear Models. These notes are suitable to follow the lectures but they should not be used as the only study material by the students.

Who did this?

Paulo Soares The author of these notes is the Professor Paulo Soares from the Departamento de Matemática at the Instituto Superior Técnico.

Disclaimer: much of this content is an adaptation (and often a plain and shameless copy!) of previous work by Prof. Giovani Silva and Prof. Ana Pires to whom I am very grateful.

How can this be used?

Creative Commons License This work is licensed under a Creative Commons Attribution-NonCommercial 4.0 International License.

21/12/2025