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Linear Models

Linear Models


3.0 Credit, 3 Lecture, 0 Lab


Theory of the Gaussian Linear Model with applications to illustrate and complement the theory; random vectors, multivariate normal, central and non-central chi-squared, t, F distributions; distribution of quadratic forms; Gauss-Markov Theorem; distribution theory of estimates and standard tests in multiple regression and ANOVA models; regression diagnostics; parameterizations and estimability; model selection and its consequences.

Course Outcomes

Upon successful completion of this course, the student will be able to:

Gaussian Linear Models

Demonstrate the application of Gaussian Linear Models for observational studies and designed experiments.

Solve problems

Solve problems using random vectors.

Understand derivation

Understand derivation and distribution of linear and quadratic forms.

Understand definitions

Understand definitions and properties of multivariate normal, non-central chi-square, t, and F distributions.

Derive maximum likelihood

Derive maximum likelihood estimates of parameters in a linear model with normal, independent errors.

Linear models estimates

Derive the properties of linear models estimates (Gauss-Markov Theorem, Wald tests).

Unconstrained and con-strained models

Derive tests on linear hypotheses by estimation of both the unconstrained and con-strained model (full and reduced LRT/ANOVA).

Cell means model

Apply the cell means model in one-way and multiway fixed designs, interpret parame- ters from alternative model reparameterizations, estimability.


Explore consequences of model assumption violations and use regression diagnostics to identify possible model violations.

Theoretical consequences

Derive theoretical consequences of overfitting and underfitting in model selection.