Department:
Statistics >
Course:
Linear Models
STAT
535

## Linear Models

### Hours

3.0 Credit, 3 Lecture, 0 Lab

### Semester

Winter
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.

## 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.