Linear Models
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.
STAT
535
 Hours 3.0 Credit, 3.0 Lecture, 0.0 Lab Prerequisites STAT 330 & STAT 340 & MATH 313 Taught Fall
Course Outcomes:

#### Course Outcomes

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

#### Understand Derivation

Understand derivation and distribution of linear and quadratic forms.

#### Understand Definitions

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

#### Derive Maximum Likelihood

Be able to derive maximum likelihood estimates of parameters in a linear model with normal, independent errors.

#### BLUE and MVUE

Understand Best Linear Unbiased Estimation (BLUE) and Minimum Variance Unbiased Estimation (MVUE) in linear models.

#### Estimation

Know how to estimate in both the unconstrained and constrained model.

#### Hypothesis Tests

Know how to implement hypothesis tests in the normal linear model.

#### Cell Means Model

Be able to implement the cell means model in one-way and multiway fixed designs.

#### Multiple Comparison

Know how to test in a multiple comparison setting.

#### Lack of Fit

Be able to derive and use measures of lack of fit and importance.

#### Sums of Squares

Understand the difference and compute Type I and Type III sums of squares.

#### Missing Cells

Understand and be able to compute tests and estimates when a design has data missing in some cells.

#### 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.