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Up: Year 2
Previous: MC262 Linear Regression Models
MC264 Linear Statistical Models
Credits: 20 
Convenor: Dr. M.J. Phillips 
Semester: 2 (weeks 1 to 12) 
Prerequisites: 
essential: MC160, MC260, MC265 

Assessment: 
Coursework: 20% 
Three hour examination: 80% 
Lectures: 
36 
Classes: 
none 
Tutorials: 
none 
Private Study: 
104 
Labs: 
10 
Seminars: 
none 
Project: 
none 
Other: 
none 
Total: 
150 


Explanation of Prerequisites
The module MC160 provides the basic ideas of probability
which are required to understand statistical methods.
The module MC265 presents the basic concept of a statistic
and its use in estimation and hypothesis testing.
The module MC260 provides the techniques for study of the
joint distributions of random variables which enable the
classical normal theory results of mathematical statistics to be derived.
Then there is a brief introduction to
the basic methods of data analysis
based on the
classical normal theory results of mathematical statistics.
Course Description
The single most important method in statistical analysis is the
natural extension of the simple linear (regression) model
to include several explanatory variables to give the general
linear model.
With a judicious choice of variables it is possible to cover,
within a general framework, a number of techniques for analysing
data: multiple linear regression, ploynomial regression,
analysis of variance (ANOVA) techniques.
Two prime objectives of an analysis using this model include
a determination of which explanatory variables are important,
and exactly how these variables are related to the response
variable. It is possible to associate confidence intervals to
estimates or predictions obtained from the model and
assign pvalues to hypotheses to be tested.
The analysis of the model is based on the method of least squares
estimation, where the `residual sum of squares' not only
provides an estimate of the error variance but, perhaps more
importantly, also offers a method for assessing the acceptability
of any proposed model.
Note: this module cannot be taken in conjunction with MC262.
Aims
This module covers the general linear model.
A brief introduction to the least
squares estimation of regression lines aims to show how
linear relationships can be established between two variables.
This module aims to present the method of least squares
estimation of the linear model parameters and the methods of
making inferences about these parameters through the calculation of
confidence intervals and the use of hypothesis tests.
In particular it is an aim of this course to impart understanding
of how statistical models explain variation.
The aim of covering the
theory for the general linear regression model is to
enable the extension of the theory
to cover multiple linear regression, polynomial regression,
analysis of variance and covariance.
This module aims to provide the necessary foundation for the
study of generalized linear models in MC361.
Objectives
To know the distributions of the least squares estimators
for parameters of the simple linear regression model.
To present the assumptions made in using the
simple linear regression model.
To enable the calculation of
confidence intervals and prediction intervals and
the use of hypothesis tests for model parameters.
To perform hypothesis tests using an analysis of variance
(ANOVA) table and to understand how it is used to explain
variation.
To assess the lack of fit of a linear model
using repeated observations.
To understand the theory of the general linear model.
To be able to apply the extra sums of squares principle to
discriminating between models.
To understand the advantages of using Latin square designs.
Transferable Skills
The ability to calculate estimates and make
inferences about the parameters of the
simple linear regression model.
The ability to construct confidence intervals
and prediction intervals and
to perform hypothesis tests for model parameters.
Knowledge of using an analysis of variance
(ANOVA) table to explain variation.
The ability to assess the
lack of fit of a linear model using repeated observations.
Knowledge of the theory of the general linear model.
The ability to apply the extra sums of squares principle to
discriminating between models.
Syllabus
Relationships between variables are considered.
Inferences about the linear association of two variables
are studied using the coefficient of correlation.
The simple linear regression model is briefly explained.
Least squares estimators of slope and intercept parameters
are obtained.
Sampling distributions are derived for these estimators as
well as for `error' variance parameter.
Inference for the model parameters is covered using confidence
intervals, prediction intervals and hypothesis tests.
Calibration.
Least squares estimators of the parameters of some other simple
models are obtained.
Use of residuals for checking model assumptions.
Analysis of variance.
Distributions of sums of squares of standard normal variables.
Lack of fit using repeated observations.
The theory of the general linear model.
Multiple regression, including polynomial regression.
Confidence intervals, prediction intervals and hypothesis tests
for these models.
Extra sums of squares principle.
An introduction to GLIM.
Oneway analysis of variance. Contrasts and orthogonal polynomials.
Twoway analysis of variance including replication.
Latin square designs.
Fitting models in GLIM.
Reading list
Essential:
W. Mendenhall, R. L. Scheaffer and D. D. Wackerly,
Mathematical Statistics with Applications,
4th edition,
Duxbury Press, 1990.
Details of Assessment
The final assessment of this module will consist of 20% coursework
and 80% from a three hour examination, which is OPEN BOOK, during the
Summer exam period. The 20% coursework contribution will be determined by
students' solutions to coursework problems. The examination paper will contain
6 questions with full marks on the paper obtainable from 4 complete answers.
Next: MC265 Introductory Statistics
Up: Year 2
Previous: MC262 Linear Regression Models
S. J. Ambler
11/20/1999