#### 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.

#### Regression

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.