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Next: MA2261 Linear Statistical Models
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Previous: MA2201 Introductory Statistics
MA2251 Linear Regression Models
Credits: 10 |
Convenor: Dr. M.J. Phillips |
Semester: 2 (weeks 1 to 6) |
Prerequisites: |
essential: MA1061, MA2201 |
|
Assessment: |
Examination and coursework: 80:20% |
Examination: 0% |
Lectures: |
18 |
Problem Classes: |
3 |
Tutorials: |
none |
Private Study: |
51 |
Labs: |
3 |
Seminars: |
none |
Project: |
none |
Other: |
none |
Surgeries: |
none |
Total: |
75 |
Subject Knowledge
Aims
This module covers the simple linear regression
model as an introduction to
the general linear model.
An 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 demonstrate
the extension of the theory
to cover multiple linear regression
and polynomial regression.
Learning Outcomes
Students should know
the distributions of the least squares estimators
for parameters of the simple linear regression
model,
be able to calculate
confidence intervals and prediction intervals and
use hypothesis tests for model parameters.
Students should be able to
perform hypothesis tests using an analysis of variance
(ANOVA) table and to understand how it is used to explain
variation, and be able
to assess the lack of fit of a linear model
using repeated observations.
Methods
Class sessions with some handouts.
Assessment
Marked problem sheets and examination.
Subject Skills
Aims
To provide students with the
ability to calculate estimates and make
inferences about the parameters of the
simple linear regression model,
and
the knowledge of using an analysis of variance
(ANOVA) table to explain variation,
as well as the
knowledge of the theory of the general linear model.
Learning Outcomes
Students will have worked on a
number of statistical problems, drawn
conclusions and have written up their
results with the aid of computer resources.
Students will be able to
use the techniques taught within the module to
answer statistical questions, and be able
to present arguments and solutions
in a coherent form.
Methods
Computer classes.
Assessment
Marked problem sheets and examination.
Explanation of Pre-requisites
The module MA1061 provides the basic ideas of probability
which are required to understand statistical methods.
The module MA2201 presents the basic concept of a statistic
and its use in estimation and hypothesis testing.
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
use of the simple linear regression model
which is
the simplest example of the general
linear model.
The prime objective of an analysis using this
model
is the determination of
how the explanatory variable
is related to the response
variable. It is possible to associate
confidence intervals to
estimates or predictions obtained from the
model and
assign p-values 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 MA2261.
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.
Reading list
Recommended:
W. Mendenhall, R. L. Scheaffer and D. D. Wackerly,
Mathematical Statistics with Applications,
6th edition,
Duxbury Press, 2002.
Resources
Problem sheets, computer laboratory, lecture rooms.
Module Evaluation
Module questionnaires, module review, year review.
Next: MA2261 Linear Statistical Models
Up: ModuleGuide03-04
Previous: MA2201 Introductory Statistics
Author: C. D. Coman, tel: +44 (0)116 252 3902
Last updated: 2004-02-21
MCS Web Maintainer
This document has been approved by the Head of Department.
© University of Leicester.