Assignment 3
Statistics 371 Solutions
1.
In this question, we look at the use of the t and F distributions in testing hypotheses
involving the coefficients of a regression model.
a)
Find (interpolate when necessary)
, a constant
c
so that
,
and a constant
d
so that
20
(
 1.90)
Pt
≥
10
(

)
0.90
c
≤=
6,30
(
1.80)
PF
≥
10,10
(

)
0.90
d
[Draw pictures if you have trouble with these calculations]
From the tables, we have
and
so
. Hence
. Using R, we get
20
(
1.725)
0.05
>=
20
(
2.086)
0.025
20
(
1.90)
0.04
>≈
20
(
 1.90)
0.08
≥≈
20
(
 1.90)
0.072
≥=
From the tables, we have
so
10
(
1.812)
0.95
10
(
 1.812)
0.90
≤
=
From tables, we have
so
. From R, we
get
6,30
(
1.98)
0.10
6,30
(
1.80)
0.10
≥>
6,30
(
1.80)
0.133
Since
, we have
and from the tables
0
F
≥
10,10
(
)
0.90
d
2.32
d
=
In a packaging trial, a market research firm decided to investigate three different colours
and two different styles of packaging leading to 6 different treatments, coded as below.
The overall purpose of the investigation was to better understand how colour and style of
packaging affected customer opinion of the product.
colour
style
treatment
x1
x2
x3
x4
x5
x6
Red
1
1
1
0
0
0
0
0
Red
2
2
0
1
0
0
0
0
Blue
1
3
0
0
1
0
0
0
Blue
2
4
0
0
0
1
0
0
Green
1
5
0
0
0
0
1
0
Green
2
6
0
0
0
0
0
1
Using a panel of 42 volunteers, they presented each of the six versions of the packaging
to 7 of the volunteers. After explaining the goal, the volunteers were each given a
questionnaire about the packaging. The response variate is the score on the questionnaire,
a number out of 100. The data are in the file ass2q2.txt.
b)
A simple model to describe the data is
01
Y
treatment
R
β
=
++
. Explain why this
simple model is a bad idea.
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View Full DocumentThe treatment number is an index, not a quantitative explanatory variate. For example
this model implies that the effect of changing from treatment 2
to treatment 3 is the same
as the effect of changing from treatment 4 to treatment 5.
Alternately, consider the model
.
2
12
3
4
5
6
123456
,
~
(
0
,
Yx
x
x
x
x
x
R
R
M
V
N
I
ββ
β
σ
=+
+
+
+
+
+
)
c)
Check the fit of the model using the four basic plots. Are any remedies required?
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 Spring '09
 AHMED
 Statistics, BMW Sports Activity Series, $1000, 200 days, 188 degrees, 193 degrees

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