STAT 420
Fall 2007
Homework #8
(10 points)
(due Friday, October 26, by 3:00 p.m.)
1.
A forester seeking information on basic tree dimensions obtains the following
measurements of the diameters 4.5 feet above the ground and the heights of 12
sugar maple trees. The forester wishes to determine if the diameter measurements
can be used to predict the tree height.
Diameter
x
(inches)
0.9
1.2
2.9
3.1
3.3
3.9
4.3
6.2
9.6
12.6
16.1
25.8
Height
y
(feet)
18
26
32
36
44.5
35.6
40.5
57.5
67.3
84
67
87.5
a)
Make a scatterplot of
x
vs.
y
. Does a straightline relationship seem appropriate?
b)
Make a scatterplot of
x
'
=
ln
x
vs.
y
'
=
ln
y
. Does a straightline relationship seem
appropriate?
c)
Fit a straightline regression to the transformed data. Add the leastsquares regression
line to the scatterplot from part(b). Comment on the adequacy of the fit.
d)
Construct a 95% prediction interval for the height of the tree
y
with the diameter
x
= 10 inches. Hint: Construct a 95% prediction interval for
ln
y
first.
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 Spring '07
 STEPANOV
 Least Squares, Regression Analysis, Prediction interval, straightline relationship, straightline regression, Mr. Fred G. Hire

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