Math 161B - Spring 2016 Homework 5 complete solutions correct answers key 

Math 161B - Spring 2016 Homework 5 complete solutions correct answers key 
1. In a study, the eects of varying two factors A and B on a response X were observed.
Factor A has two levels (A1 and A2). Factor B has three levels (B1;B2; and B3).
For each combination of factor level, one response value was observed. The observed
data are recorded in the table below.
Factor B
Factor A B1 B2 B3
A1 32 28 33
A2 40 30 41
(a) We will t an additive ANOVA model of the form
Xij = + i + j + ij
Find the estimates of ; 1; 2; 1; 2; 3 for this data.
(b) Find the value of the residual 11.
(c) Draw a line plot of the raw data (by hand). That is, put factor B's levels on
the x-axis, the response on the y-axis and use either dierent colors or dierent
line styles to connect the three dots corresponding to levels 1 and 2 of factor
A. (See page 40 of notes for an example of such a plot. We usually choose to
put the factor with more levels on the x-axis).
(d) Using your estimated factor eects (^; ^i; ^ j) from part (a), compute the pre-
dicted response values
^X
ij = ^ + ^i + ^ j
Draw another line plot of these tted values.
(e) Explain why the two lines are parallel in the line plot of the tted values.
2. Rugby football is a popular quasi-amateur sport widely played in the United King-
dom, France, Australia, New Zealand and South Africa. It is rapidly gaining popu-
larity in the US, Canada, Japan and parts of Europe. Typically, a game consists of
bursts of activity which terminate when points are scored, if the ball is moved out of
the eld of play or if an infringement of the rules occurs. In 1992 some of the rules
of the game have been changed, with the aim of making play more exciting. The
data in the le \Rugby.txt" (posted on the homework website) contain the duration
(in seconds) of each passage of play in the game for ten games of New Zealand's
national team. The rst ve games studied were the last international games played
under the old rules, and the second set of ve were the rst internationals played
under the new rules.
(a) Create a meaningful graphical display of the data and describe what you see.
(b) Use a one-factor ANOVA analysis to test whether the rule change had an eect
on the mean time of play passages.
(c) Check the assumptions of the ANOVA model you t in (b). Discuss whether
or not the assumptions are approximately satised in this model (support your
discussion by relevant SPSS output).
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Math 161B - Spring 2016 Homework 5
(d) Log-transform the response variable. Fit a new ANOVA model on the trans-
formed response and check once again the ANOVA assumptions for the new
model. Which assumption(s) (if any) are you still worried about? Present
relevant SPSS output to support your ndings.
(e) Formulate a conclusion corresponding to the p-value read o from the ANOVA
table produced by SPSS (cite the p-value).
(f) Can we say that the rule change made a signicant dierence for the mean time
of play passages? Why or why not? Support your answer with relevant SPSS
output.
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