Stat 512  Assignment 3
Due Monday, March 29
1.
Adapted from Kuehl, Exercise 6.3
. A study was conducted to assess the effect
of temperature on the shrinkage of dyed fabric. Four temperatures were ap
plied to four different fabrics in a 4
×
4 crossed design with
n
= 2 replications
per cell. The response variable is the percent shrinkage. The data are shown
below.
Temperature
Fabric
210
◦
F
215
◦
F
220
◦
F
225
◦
F
1
1.8, 2.1
2.0, 2.1
4.6, 5.0
7.5, 7.9
2
2.2, 2.4
4.2, 4.0
5.4, 5.6
9.8, 9.2
3
2.8, 3.2
4.4, 4.8
8.7, 8.4
13.2, 13.0
4
3.2, 3.6
3.3, 3.5
5.7, 5.8
10.9, 11.1
Data for this problem are available in the file
FabricShrink.txt
. The data
can be entered into R by typing
> FabricShrink < read.table("FabricShrink.txt", header=T)
at the R command prompt. Then be sure to change the variables
fabric
and
temp
into factors.
(a) Plot the response variable
y
versus each factor, and comment on what
you see.
(b) Fit the twoway ANOVA model using
y
as the response. Are the effects
of the two factors additive?
(c) Compute the mean for each level of
temp
(the
¯
Y
·
j
·
’s) and plot them.
Decompose the SS for main effect of
temp
into independent SS’s corre
spnding to linear, quadratic and cubic contrasts. Which of these trends
are significant?
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 Spring '11
 John
 Statistics, eye contact, Das Model

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