# Linear Models

### 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.