# Matrix Algebra and Linear Models (BIOM4003)

## UNIT OF STUDY

In order to obtain a deeper understanding of statistics it is necessary to learn more about matrices as used to develop and explain statistical and mathematical concepts. Matrices are not just used in statistics: they find use in mathematical models in biology (e.g. age structured population growth models), engineering (e.g. structural perturbation analysis), and economic models (e.g. decision analysis). There are three aims to this unit. Firstly, we will revise matrices learnt in earlier units and then introduce new concepts such as special matrices (symmetric, orthogonal, idempotent), rank, eigenvalues and eigenvectors, as well as some matrix and vector calculus. The second aim is to apply these techniques to the formulation of linear models and linear mixed models which have been introduced in earlier units. The underlying theory will be developed along with more advanced applications. The third aim is to provide an introduction to key application areas for the future; (i) the analysis of big datasets, ones with many predictor variables, and (ii) the analysis of spatial data. Furthermore, the students will be introduced to R, an open source statistical software package.

## Further unit of study information

### Classes

1x3 hr workshop/wk, 3x1 day workshops (exam period)

### Assessment

2 × Data Analysis Projects (50% each)

### Textbooks

Textbooks: None. Many reference books such as:

Draper, N.R., and Smith, H. (1981). Applied Regression Analysis, Second edition. N.Y.: Wiley

Graybill, F.A. (1969). Introduction to Matrices with Applications in Statistics. Belmont: Wadsworth

Harville, D.A. (1997). Matrix Algebra from a Statistician's Perspective. New York: Springer

Healy, M.J.R. (1986). Matrices for Statistics. Oxford: Clarendon

Mead, R. (1988). The Design of Experiments. Cambridge: Cambridge U.P

Neter, J., Wasserman, W., and Kutner, M.H. (1985). Applied Linear Statistical Models. Homewood, Il.: Irwin

Searle, S.R. (1982). Matrix Algebra Useful for Statistics. N.Y.: Wiley

### Faculty/department permission required?

Yes

## Unit of study rules

### Prerequisites and assumed knowledge

ENVX3002

## Study this unit outside a degree

### Non-award/non-degree study

If you wish to undertake one or more units of study (subjects) for your own interest but not towards a degree, you may enrol in single units as a non-award student.

### Cross-institutional study

If you are from another Australian tertiary institution you may be permitted to underake cross-institutional study in one or more units of study at the University of Sydney.