STAT 535
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Linear Models
Statistics
College of Computational, Mathematical & Physical Sciences
Course Description
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.
When Taught
Winter
Min
3
Fixed
3
Fixed
3
Fixed
0
Title
Course Outcomes
Learning Outcome
Upon successful completion of this course, the student will be able to:
Title
Gaussian Linear Models
Learning Outcome
Demonstrate the application of Gaussian Linear Models for observational studies and designed experiments.
Title
Solve problems
Learning Outcome
Solve problems using random vectors.
Title
Understand derivation
Learning Outcome
Understand derivation and distribution of linear and quadratic forms.
Title
Understand definitions
Learning Outcome
Understand definitions and properties of multivariate normal, non-central chi-square, t, and F distributions.
Title
Derive maximum likelihood
Learning Outcome
Derive maximum likelihood estimates of parameters in a linear model with normal, independent errors.
Title
Linear models estimates
Learning Outcome
Derive the properties of linear models estimates (Gauss-Markov Theorem, Wald tests).
Title
Unconstrained and con-strained models
Learning Outcome
Derive tests on linear hypotheses by estimation of both the unconstrained and con-strained model (full and reduced LRT/ANOVA).
Title
Cell means model
Learning Outcome
Apply the cell means model in one-way and multiway fixed designs, interpret parame- ters from alternative model reparameterizations, estimability.
Title
Regression
Learning Outcome
Explore consequences of model assumption violations and use regression diagnostics to identify possible model violations.
Title
Theoretical consequences
Learning Outcome
Derive theoretical consequences of overfitting and underfitting in model selection.
