Example

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Example Black Cherry Trees
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Example Black Cherry Trees
The data frame trees is made available in R
with gtdata(trees) and contains the well-known
black cherry trees data. These record the girth
in inches, height in feet and volume of timber in
cubic feet of each of a sample of 31 felled black
cherry trees in Allegheny National Forest,
Pennsylvania. Note that girth is the diameter of
the tree (in inches) measured at 4 ft 6 in above
the ground.
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We treat volume as the (continuous) response
variable y and seek a reasonable model describing
its distribution conditional on the explanatory
variables girth and height. This might be a
first step to prediction of volume based on
further observations of the explanatory
variables. Consider the R command gtpairs(trees,
main "trees data")
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The relationship between girth and volume is
especially noticeable. We therefore consider
first a linear model Yia bxi ei where Y is
volume and x is girth
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The R command for fitting linear models by least
squares is lm. We have gt trees.model.1
lm(VolumeGirth, datatrees) gt summary(trees.model
.1)
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The fitted model is volume -36.9 5.07
girth residual Now try gt plot(VolumeGirth,
datatrees) gt abline(coef(trees.model.1)) gt
plot(resid(trees.model.1)Girth,
datatrees, ylab"residuals from Model 1")
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