Introduction to Linear Models and Regression

Syllabus:

i) Multivariate distributions and properties; Multivariate densities; Independence, marginal and conditional distributions; Distributions of functions of continuous random vectors; Examples of multivariate densities: Dirichlet and multivariate normal distributions; Transformations and quadratic forms.
ii) Review of matrix algebra involving projection matrices and matrix decompositions; Fisher-Cochran Theorem.
iii) Simple linear regression and Analysis of variance.
iv) General linear model, Matrix formulation, Estimation in linear model, Gauss- Markov theorem, Estimation of error variance.
v) Testing in the linear model, Analysis of variance.
vi) Partial and multiple correlations, Multiple comparisons.
vii) Stepwise regression, Regression diagnostics.
viii) Odds ratios, Logit model.
ix) Splines and Lasso.

Reference Texts:

(a) Sanford Weisberg: Applied Linear Regression.
(b) C R Rao: Linear Statistical Inference and Its Applications.
(c) George A F Seber and Alan J Lee: Linear Regression Analysis.

https://www.isibang.ac.in/~adean/infsys/database/Bmath/LMR.html