Stat/F&W/Hort 572 Ane January 22, 2009
Assignment #2 — Due Friday, Feb. 6, 2009, by 4pm
Turn in lecture, discussion, or to your TA’s mailbox. Please circle the discussion section you expect to pick up
this assignment:
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Instructions. In a write-up of your solution to this assignment, you do not need to include graphs in your
solution unless the questions specifies this explicitly. You do not need to show Rcode used to create graphs.
In questions that require you to fit a model and comment on estimated coefficients, your solution should
describe the fitted model in an equation with words and units that is distinct from any Rcode used to fit the
model. For example, from the bats data set we discussed in lecture, we could express the model for fitting the
energy requirements for a bird of as a function of its mass as follows:
energy in Watts = 3.32 + 0.0678 ×(mass in grams −260)
Your solution should then also include a summary of the Rcode you used to fit the model and summarize the
results. You should edit the Routput to eliminate material that is not necessary to answer the question. For
example, if you use the summary function, you might choose to include in your solution the table of estimated
coefficients, but you should eliminate the excess output such as quantiles of residuals.
Background. A samara is the winged fruit from a tree that falls to the ground with a helicopter-like motion. A
forest scientist is interested in predicting the terminal velocity of falling samaras based on disk loading, the mass
of a samara divided by the area of the disk it passes through while spinning. A lower velocity could be related to
a larger average dispersal distance allowing samara to drop further from the maternal tree, potentially decreasing
competition for new resultant seedlings.
The scientist collected from 25–30 samaras from each of seven species and measured the disk loading and
terminal velocity of each. The species were white ash (Fraxinus americana), green ash (F. pennsylvanica), tulip
tree (Liriodendron tulipifera), sugar maple (Acer saccharum), boxelder (A. negundo), red maple (A. rubrum), and
silver maple (A. saccharinum). Samaras from the two ash species and the tulip tree are bilaterally symmetric and
roll as they spin. In contrast, the samaras from the maples and the boxelder (genus Acer ) are asymmetric and
they do not roll as they spin. Theoretical study of helicopter rotors suggests that the terminal velocity should be
linearly related with the square root of the disk loading.
The data set for this assignment is on the course web page and is named samara.txt. The columns are:
species: the common name of the species of tree
genus: the scientific genus
velocity: the terminal velocity in centimeters per second
mass: the mass of the samara in milligrams
area: area of the disk while spinning in square-centimeters
loading: the ratio of mass to area
symmetry: a factor indicating if the samara are bilaterally symmetric or not
