STAT 572 Discussion 4
TA Meng Song
Office 1270 MSC
Phone 262-3230
Email [email protected]
Office hour 11:00-12:00 AM and 1:00-2:00 PM Tue.
My Website www.stat.wisc.edu/∼songm
1 Problem 1
The following data is collected to study the relationship between frequency of chirps made
by a ground cricket and the corresponding ground temperature. The frequency is measured
as the number of wing vibrations per second.
chirps (/second) 20.0 16.0 19.8 18.4 17.1 15.5 14.7 17.1 15.4 16.2 15.0 17.2 16.0
17.0 14.1
temperature (F) 88.6 71.6 93.3 84.3 80.6 75.2 69.7 82.0 69.4 83.3 78.6 82.6 80.6
83.5 76.3
(a) Fit a linear model to predict chirps from temperature. What are the slope and intercept
of the model?
(b) Fit another linear model, using a linear transformation to centralize the explanatory
variable. What are the slope and intercept of the model?
(c) Fit another linear model, using a linear transformation to centralize and standardize the
explanatory variable. What are the slope and intercept of the model?
(d) Use these three models to predict chirp frequency under similar conditions when the
temperature is 88 F.
2 Problem 2
In the early 1990s, scientists became concerned about rapid declines in populations of am-
phibians worldwide. After some analysis, researchers consider global atmospheric causes,
such as thinning of the ozone layer and the resulting increased exposure to damaging ultra-
violet (UV-B) light to be the answer.
Rana cascadae is a kind of amphibians who lay eggs in open shallow water which is highly
exposed to sunlight. Therefore the effect of UV-B could be explained by the damage over
eggs. Researchers place Rana eggs under UV-B treatments having three levels: (a) a UV-B
blocking filter; (b) a UV-B transmitting filter; and (c) no filter. Percentage of eggs failing
to hatch (perF) is calculated at two sites:
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