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Homework 1 for Regression
Section 7454/7459
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1. When paleontologists identify a new species of dinosaur, it’s often the case that they ﬁnd only a few
bones, rather than an entire skeleton. Still, they are usually able to ﬁgure out some basic facts, such
as how big their new species of dinosaur was. They do this by comparing their new bones to the
corresponding bones of related species whose sizes are already known.
Suppose paleontologists discover a femur (thigh bone) for a new species of dinosaur. This femur is 0.33
m long. Shown below are the femur lengths and overall lengths of ten species that the paleontologists
believe are closely related to their new species.
(
X
)
(
Y
)
Species
Femur (m)
Overall (m)
1
0.27
3.6
2
0.35
6.2
3
0.49
7.7
4
0.26
4.8
5
0.51
7.0
6
0.30
5.4
7
0.38
5.9
8
0.57
8.1
9
0.23
3.5
10
0.32
5.7
●
●
●
●
●
●
●
●
●
●
0.25
0.35
0.45
0.55
4
5
6
7
8
Femur Length (m)
Overall Length (m)
(a)
i. Calculate the regression equation using the following information:
¯
X
= 0
.
368
,
S
X
= 0
.
1172
,
¯
Y
= 5
.
79
,
S
Y
= 1
.
56
,
r
= 0
.
934
.
(So that you can check your work, part of your answer should be that
a
= 1
.
22
.
)
ii. Calculate the predicted overall length for Species 4 in the data set.
iii. Calculate the residual for Species 4 in the data set.
iv. Calculate the predicted overall length for the paleontologists’ new species. (Recall that its
femur is 0.33 m long.)
v. Suppose that some other paleontologists discover another femur with a length of 0.87 m from
another new species that is also related to the species in this data set. Explain why it would
be inappropriate to use the results of our regression to predict the length of this other new
species.
(b)
i. We can calculate that
SS
Regr
= 19
.
04 and
SS
Res
= 2
.
77
.
(You don’t have to check this.) Use
this information to construct the regression ANOVA table.
1
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 Spring '08
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