Department of Mathematical and Computational Sciences
No late assignments will be accepted.
As in all work in this course, 5% of your grade is for quality of presentation, including
the use of good English, properly commented and easy-to-understand programs, and clear
proofs. In general, short, simple answers are worth more than long, complicated ones. Un-
less stated otherwise, all answers should be justi ed. The TA has a limited amount of time
to devote to each assignment, so what you hand in should be well-organized and easy to
evaluate. You are encouraged to type your assignment answers in Latex or Word, but legible
handwritten and well presented answers are also acceptable.
Your R programs and their outputs, as well as your written answers, will be marked. Your
programs should conform. to the usual coding standards for comments, good programming
style, etc. You should format the output from your program so that it is easy for your TAs
to read and to understand your results.
Hand in ve les: the source code (text le) of all your R programs, a pdf le of gures
generated by the programs, a text le of all printed output, a pdf le of answers to all the
questions, and a scanned, signed copy of the cover sheet at the end of the assignment. The
ve les should be submitted using https://submit.utm.utoronto.ca/utorsubmit/.
Be sure to indicate clearly which question(s) each program and piece of output refers to. All
the R code (functions and script) for a given question should appear in one location in your
source le, along with a comment giving the question number. All material in all les should
appear in order; i:e:, material for Question 1 before Question 2 before Question 3, etc. It
should be easy for the TA to identify the material for each question. In particular, all gures
should be titled, and all printed output should be identi ed with the Question number. The
four les should be submitted electronically. In addition, if we run your source le, it should
not produce any errors, it should produce all the output that you hand in ( gures and print
outs), and it should be clear which question each piece of output refers to. Output that is
not labled with the Question number will not be graded. Besides the electronic submission,
an identical printed copy of your assignment must be also be submitted on Thursday March
22, at the beginning of lecture (sharp).
I don’t know policy: If you do not know the answer to a question (or part), and you
write \I don’t know", you will receive 20% of the marks of that question (or part). If you
just leave a question blank with no such statement, you get 0 marks for that question.
Question 1
Show that the fundamental equations for the one way analysis of variance (ANOVA)
for SST and SSTreatments can be written as
N (2)
Question 2
Show that the fundamental equations for the two way analysis of variance (ANOVA)
for SST, SSA, SSB,and SSAB, can be written as
Question 3
Do problem 5.3.a from your textbook (8th edition) using the statistical software package R
without the question regarding model’s adequacy. Present interaction plots with interpreta-
tion and discussions. Use Tukeys test to determine which levels of the pressure factor are
signi cantly di erent.
Question 4
Do problem 5.19 from your textbook (8th edition) using the statistical software package R
without the question regarding model’s adequacy.
Question 5
Do problem 4.14 from your textbook (8th edition) using the statistical software package R
without the question regarding model’s adequacy.
Question 6
Do problem 4.23 from your textbook (8th edition) using the statistical software package R.
Question 7
Do problem 4.40 from your textbook (8th edition) using the statistical software package R.
3
University of Toronto Mississauga
STA305H5S - Experimental Design
Cover sheet for Assignment 1
Complete this page and hand it in with your assignment.
Name:
(Underline your last name)
Student number:
I declare that the solutions to Assignment 1 that I have handed in
are solely my own work, and they are in accordance with the University
of Toronto Code of Behavior. on Academic Matters.
Signature: