IITM BS Linear Statistical Models (BSMA3012): Syllabus and Tips

Linear Statistical Models (BSMA3012) is a 4 credit degree level elective on the theory of linear models. You study least squares, best linear unbiased estimates, the Gauss-Markov theorem, testing linear hypotheses and ANOVA. Ideas are shown with examples, data sets and exercises in R. There are no prerequisites. The instructor is Siva Athreya, Professor at the International Centre for Theoretical Sciences (TIFR) and the Indian Statistical Institute, Bangalore Centre.

The course page and the handbook agree. The handbook's degree level table (updated 18 March 2026) lists it as a DEGREE course with the SE tag, 4 credits and no prerequisite. The handbook does not explain SE.

What you learn

• Weeks 1 and 2: review. Estimation and hypothesis testing, and working with R.
• Weeks 3 to 7: least squares theory. Least squares estimation, which linear functions can be estimated, normal equations, best linear unbiased estimates (BLUEs), the Gauss-Markov theorem, degrees of freedom and the fundamental theorems of least squares.
• Weeks 8 to 10: testing and classification models. Testing linear hypotheses, one-way and two-way classification models, ANOVA and ANCOVA.
• Weeks 11 and 12: beyond the basic model. Nested models, multiple comparisons and an introduction to random effects models.

In short, the course asks why least squares works, when its estimates are the best possible, and how to test claims about a model with proper statistics.

How it is assessed

The course page lists 12 weeks of coursework, weekly online assignments, 2 in-person invigilated quizzes and 1 in-person invigilated end term exam. It does not mention an OPPE or a project.

Where it counts

• Degree level elective. It fills 4 elective credits. See the DS electives list.
• BSc elective credits. Its 3xxx code makes it a level 3 course under the handbook's rule. The BSc fee table shows level 3 credits can fill the 8 BSc elective credits. See the BSc degree level.
• No minor. It is not in any minor list.
• Term plan. The March 2026 table marks it as offered only in September 2026, out of May 2026, September 2026 and January 2027.

How it compares with Linear Models with Applications

The same instructor teaches Linear Models with Applications (BSMA3015). The two share early topics such as least squares, BLUEs and the Gauss-Markov theorem.

The handbook does not say whether you can count both toward your degree. Ask support before you register for the second one.

Who finds it hard and how to prepare

Much of this course is linear algebra applied to statistics. If rank, null space and projections from Maths 2 have faded, normal equations and estimable functions will feel confusing. If R is new to you, the weekly exercises take longer.

• Revise Maths 2 weeks 3 to 8. Rank, null space, inner products and projections. Least squares is a projection, and once you see that, many results are easier to follow.
• Revise Stats 2 estimation and testing before week 1, so the review weeks feel like a recap and not new content.
• Set up R early. Install it and fit a simple linear regression on a small data set before the term.
• List the assumptions. For every theorem, write down what it assumes. The Gauss-Markov theorem and the testing results only hold under their assumptions.
• Use the suggested books. Plane Answers to Complex Questions: The Theory of Linear Models by R. Christensen, and Linear Statistical Inference by C. R. Rao.

What to take before and after

• Before: Maths 2 and Stats 2 from the foundation level. The IITM BS statistics guide is a good refresher.
• After: Statistical Computing looks at regression from the computing side, with regression as maximum likelihood and penalised regression.

Common questions

Do I need to know R before the course?

No prerequisite is listed, and week 2 reviews working with R. Still, a few hours of basic R before the term makes the weekly exercises much easier.

How is this different from regression in the diploma ML courses?

The diploma courses teach you to fit models and predict, for example linear regression in scikit-learn. This course proves properties of the estimates and tests hypotheses about the model. It is about why, not only how.

Is it offered every term?

No. The March 2026 table marks it only for September 2026 among the three listed terms. Offering also depends on registrations.