28177 - Statistical Models

Learning outcomes

By the end of the course the student should know the basic theory of normal linear models and generalized linear models. In particular the student should be able: - to define a statistical model - to formulate the normal linear model, estimate its parameters and test their significance - to use the variable selection procedures - to define a generalized linear model, by combining a random component with a linear predictor with a proper link function - to estimate and test the significance of the parameter of a generalized linear model - to evaluate the goodness of fit of a model and to detect violations of model assumptions

Course contents

• Basic framework for linear models
  • model specification and assumptions;
  • parameter estimation: least squares and maximum likelihood methods;
  • coefficient of determination R2: definition and properties;
  • finite and asymptotic properties of the estimators;
  • hypothesis testing on regression coefficients.
• Regression diagnostics
  •  residuals: definitions and properties;
  • Influential observations and leverage points;
  • Multicollinearity
• Model selection
  • effects of model mispecification;
  • stepwise methods;
  • best subset selection.
• Inclusion of qualitative regressors
  • dummy variable coding;
  • interactions between regressors.
• Some special cases
  • one-way ANOVA;
  • two-way ANOVA.
• Generalized linear models
  • general definition: linear predictor, link function, random component;
  • maximum likelihood estimation;
  • hypothesis testing on model parameters.

Readings/Bibliography

Recommended readings (a detailed list of selected chapters and sections in available on virtuale.unibo.it):

Kutner, M. H., Nachsteim, C. J., Neter, J., Li, W. (2005). Applied Linear Statistical Models (5th edition). McGraw-Hill.

Montgomery, D. C., Peck, E. A., Vining, G.G. (2021) Introduction to linear regression analysis. Sixth edition. Wiley.

Handouts provided by the teacher.

Other readings:

Brown, J. D. (2015). linear Models in Matrix Form. Springer.

Fox J. (2016). Applied Regression Analysis and Generalized Linear Models (3rd edition). Sage.

Weisberg S. (2005). Applied Linear Regression. Wiley, third edition.

Teaching methods

The course is delivered through lectures and practical sessions.

Lectures combine theoretical explanations with the guided analysis of real-world examples.

Practical sessions are an integral part of the course and provide opportunities to apply the concepts introduced during the lectures using R. They are organized according to a flipped classroom approach. Before each practical session, students are expected to prepare independently using the materials made available on Virtuale, including Moodle Books and readiness quizzes.

During the practical sessions, students work in small groups of two or three on a set of statistical and computational tasks. The instructor supports their work by providing guidance and progressive feedback and by discussing the proposed solutions with the class. Therefore, the practical sessions do not consist of step-by-step demonstrations of complete solutions, but require students to take an active part in identifying suitable methods, writing and checking R code, and interpreting the results.

Students are strongly encouraged to complete the preparatory activities before attending each practical session, as the work carried out in class is based on the knowledge and skills introduced in the pre-class materials.

All students must attend Module 1, 2 on Health and Safety online

Assessment methods

The exam will assess each student's knowledge and skills at both the theoretical and practical levels.

The use of AI or smart devices (including, but not limited to, smartphones, smartwatches, smart glasses, and earbuds) during the exam is strictly prohibited. Any such use constitutes a violation of academic integrity and will be reported to the appropriate University authorities for disciplinary review.

The exam consists of two mandatory parts, both of which must be completed during the same exam sitting.

The first mandatory part consists of a written exam containing a set of multiple-choice and open-answer questions on the models presented during the course. These questions cover both theoretical aspects and R commands or output produced using the R software. Multiple-choice questions are graded as follows: each correct answer is awarded 1 point, each incorrect answer is penalized by 0.20 points, and unanswered questions receive 0 points. Each open-answer question is awarded between 0 and 2 points, depending on the correctness of the answer and the appropriateness of the terminology used. The number of multiple-choice and open-answer questions may vary from one exam sitting to another, while the maximum score remains fixed at 24 points. Students will have 60 minutes to complete the written exam. Consulting textbooks or personal notes during the written exam is not permitted.

For the first exam sitting after the end of the course, students may choose to split the written exam into two partial exams, each lasting 30 minutes and worth a maximum of 12 points. The first partial written exam takes place after the first five weeks of the course and covers the topics presented during the first part of the course. The second partial written exam is scheduled after the end of the course and covers the topics presented during the second part of the course. Students must take both partial written exams. In particular, to register for the second partial written exam, a student must have taken the first partial written exam (no minimum score is required). Furthermore, students who take the first partial written exam are not allowed to take the full written exam during the first exam sitting after the end of the course.

The second mandatory part is a computer-based practical exam. The practical exam assesses a student's ability to use R to solve a practical problem. Students will be required to write an R script and report the results obtained using that script. The practical exam is graded on a scale from 0 to 7 points, depending on the correctness of the solution and the quality and correctness of the corresponding R script. Students will have 30 minutes to complete this part of the exam. During the practical exam, students may consult a printed copy of the computer lab session handouts.

The final mark is obtained by adding the scores from the written and practical exams. An additional bonus is assigned based on the number of practical sessions attended by the student:

- 0-4 practical sessions: 0;

-5 practical sessions: 0.6;

- 6 practical sessions: 0.8;

- 7 practical sessions: 1.

Non-integer final marks are rounded down to the next lower integer. Overall marks larger that 30 but lower than 31 are rounded down to 30. Final marks larger or equal than 31 are recorded as 30 cum laude.

In the event of failure or rejection of the final mark, students must repeat the entire exam at one of the subsequent exam sittings. Students may reject a passing grade and retake the exam at least once but no more than twice.

Teaching tools

Course materials, lecture slides, datasets, R scripts, representative assessment tasks with solutions, guidance on the use of the recommended readings, and class lecture recordings (excluding practical sessions) will be made available through Virtuale. Students are expected to consult the platform regularly before and after each class to prepare for practical sessions.

Office hours

See the website of Giuliano Galimberti