STAT3912
Semester 1
Applied Linear Models (Adv)
2012
Assignment 2 Solutions
1. First write
q
1
1
nY = Y1 + . . . + Yn ,
n
n
(x1 x)
(xn x)
SXX 1 =
Y1 + . . . +
Yn ,
SXX
SXX
and
S0 =
n
X
yi2 nY 2 12 SXX .
i=1
Let A be an orthogonal matrix with first row
T
Lecture 1 - Outline
It all begins with a question . . .
The important thing is not to stop questioning.
Albert Einstein (1879 - 1955)
Fact: too many scientific projects do not have a well defined major question!
Applied Linear Models: Lecture 1
1
Knowledg
Lecture 21 Introduction to the design of experiments
22. Introduction to Design of Experiments part
The second part of STAT 3012/3912 is concerned with the planning and analysis
of experiments.
New concepts
Simple designs for comparing one factor
We wi
UNIVERSITY OF SYDNEY
SCHOOL OF MATHEMATICS AND STATISTICS
STAT 3912: Applied Linear Models (Advanced)
1. Introduction
The independent random variables Y1 , Y2 , , Yn are said to satisfy a linear model if they
can be expressed in the form
Yi = xi1 1 + + xi
Lecture 21 Introduction to the design of experiments
New concepts
Simple designs for comparing one factor
Complete randomized design
Block design, RCBD
Systematic design
Design generation
Applied Linear Models: Lecture 21
1
22. Introduction to Design
STAT 3012/3912 Applied Linear Models m Semester 1, 2012
Quiz (Monday, 23/04/12)
a
Time allowed: 40 minutes
Reading; time: 2 rnirmtes
Notes and Instructions:
0 This Quiz is assessed. It carries weight 10% towards your nal mark for STAT3012 and
6% for STAT3
STAT3012 Assignment 1
Feedback and Solutions
User:
April 10, 2012
The comments and code below show one way of tackling the assignment questions. The
methods used by students were many and varied, showing the versatility of the R program.
A marking scheme
STAT 3012/3912 Applied Linear Models Semester 1, 2012
Assignment (due by Wednesday, 4/04/12, 10am)
Hand in a printed pdf report using process() of less than 15 A4 pages. Otherwise penalties
will be incurred.
Correctness, conciseness, presentation, reason
STAT 3012/3912 Applied Linear Models Semester 1, 2012
Assignment (due by Friday, 18/05/12, 2pm)
Problems
Hand in an assignment report of no more than 8 pages. Correctness, presentation, reasoning
and working will contribute towards the final mark. A marki
STAT3912
Semester 1
Applied Linear Models (Adv)
2012
Assignment 1 Solutions
1. (a) The X matrix is
1
.
.
.
1
X=
0
.
.
.
0
.
.
0
1
.
.
0 1
where the first row is repeated n times and the row (0 1) repeated m times.
(b) In this case
n 0
0 m
T
(X X
STAT 3012/3912 Applied Linear Models Semester 1, 2012
Tutorial & Lab Week 03 Solutions
Solutions for Tutorial Problems
1. First for the simple linear regression model and for X = X
1P 2
1
xi
x
T
1
n
(X X) =
,
x
1
SXX
where SXX =
P
P
x2i ( xi )2 /n. Thus
STAT 3012/3912 Applied Linear Models Semester 1, 2012
Tutorial & Lab Week 04 Solutions
Solutions for Tutorial Problems
1. (a) An estimate for 2 is
2 = 0.674/(8 3) = 0.1348.
(b) A 95% CI for 1 is
0.09 t5 (0.975)
0.00147
i.e. 0.09 0.036.
(c) Test H0 : 2
STAT 3012/3912 Applied Linear Models Semester 1, 2012
Tutorial & Lab Week 02 Solutions
Solutions for Tutorial Problems
1. (a) Observational.
(b) Factor 1 = average expenditure for research and development over last three years.
Three levels: low, moderate
Lecture 1 - Outline
Knowledge based on evidence
The scientific method is about getting knowledge based on (hard) evidence,
which involves the following steps:
It all begins with a question . . .
1. Formulate question
2. Collect relevant data
3. Do statis