MAT 3378 Assignment 5 :
1. Consider a balanced two factor nested design, where only factor B has
random eects. Consider the mean of the responses within the level i of
factor A, that is
b
n
1
Y i =
Yijk .
n b j=1
k=1
A consequence of the mixed (i.e. a xed
MAT 3378 Assignment 1 Solutions
[8]
Question 1:
1. (a) The response variable is the amount of wear of a tire. An explanatory
variable is the rubber compound. We can also imagine that the car
itself could have an eect on the wear of the tire. However, it s
MAT 3378
Assignment 2 :
Question 1: There is an ANOVA table found below. It is from an experiment with a completely randomized design with 4 treatments and a total of 16
observations of the response variable.
source
Treatment
Error
Total
df
SS
MS
146.056
MAT 3378
Assignment 1
Question 1 :
1. Un ingnieur dautomobile sest intress ` leet de quatre composs de
e
e
ea
e
caoutchouc sur la dure de vie des pneus dautomobile. Pour mener `
e
a
bien ltude, cinq pneus ont t fabriqus ` partir de chacun des quatre
e
ee
MAT 3378
Assignment 1 :
Question 1:
1. An automotive engineer was interested in the eect of four alternative
rubber compounds on the life of automobile tires. To carry out the study,
ve tires were manufactured from each of the four compounds and ve
automo
MAT 3378 Assignment 5 Solutions
[10]
1.
We will use the properties of the covariance operator to show that
2 cfw_Y i =
2
2 + n
.
nb
Proof:
2 cfw_Y i = cfw_Y i , Y i
1 b n
1
Y ijk ,
=
n b
nb
j=1
k=1
=
1
nb
n
b
2
n
b
n
Y ij
k
j =1 k =1
b
cfw_Yijk ,
MAT 3378
Midterm Examination
Duration: 105
minutes
Student Number:
Last Name:
First Name:
This is a closed book examination. However one formula sheet
is permitted.
Only non-programmable and non-graphic calculators are permitted.
The exam will be marke
MAT 3378 Assignment 4
)
1. Kidney failure patients are commonly treated on dialysis machines that
lter toxic substances from the blood. The appropriate dose for eective
treatment depends, among other things, on duration of the treatment and
weight gain be
MATH 3378
Midterm Examination (Solutions)
[5]
1. An experiment with a completely randomized design was run to determine whether four specic ring temperatures aect the density of a
certain type of brick. Overall the experiment yielded for nT = 13 experimen
MATH 3378
Midterm Examination
Duration: 105
minutes
Student Number:
Last Name:
First Name:
This is a closed book examination. However one formula sheet
is permitted.
Only non-programmable and non-graphic calculators are permitted.
The exam will be mark
MAT 3378
Assignment 3
Question 1: Consider the SENIC data from Appendix C.1. The variables
are explained on page 1348. We would like to know if the mean length of stay
(variable 2) is the same in the four geographic regions (variable 9).
(a) Write an appr