Stat 301
Lab 9: Due November 17
Fall 2014
In a study of plant communities in tropical forests, researchers quantified the
nonstructural carbohydrate (NSC) concentration (mg/g) and sugar concentration (mg/g)
in stems of different species of trees and shrubs in moist semi-evergreen and dry
deciduous tropical forests in the rainy season in Bolivia. NSC is stored in plant stems
and may allow plants to overcome periods of stress and thus enhance survival. The sugar
concentration in plants is an important consideration if one wants to use the plant material
to make ethanol. The researchers are interested in using the NSC concentrations to
predict the concentration of sugar (mg/g) in tropical trees and shrubs. The data can be
found on the course website www.public.iastate.edu/~wrstephe/stat301.html. In order to
make things more interpretable, (NSC – 100) will be used as one explanatory variable. A
second explanatory variable is an indicator (dummy) variable for the type of forest:
Forest Indicator = 1 if the sampling stems are from a moist semi-evergreen tropical forest
and Forest Indicator = 0 if the sampling stems are from a dry deciduous tropical forest.
1. Consider the entire set of data for stems of different species of trees and shrubs from
both moist and dry forests together. Use Fit Y by X to fit separate regression lines for
moist and dry forests relating sugar concentration to (NSC – 100).
a) How much of the variability in the sugar concentration for dry tropical forest trees
and shrubs is explained the by the linear relationship with the amount of NSC?
b) What is the estimate of the error standard deviation?
c) Give the least squares prediction equation for predicting sugar concentration in
dry tropical forest trees and shrubs from (NSC – 100).
d) Give an interpretation of the estimated intercept for dry tropical forest trees and
shrubs.
e) Give an interpretation of the estimated slope coefficient for dry tropical forest
trees and shrubs.
f) Is there a statistically significant linear relationship between (NSC – 100) and
sugar concentration for dry tropical forest trees and shrubs? Support your answer
statistically.
g) How much of the variability in the sugar concentration for moist tropical forest
trees and shrubs is explained the by the linear relationship with the amount of
NSC?
h) What is the estimate of the error standard deviation?
i) Give the least squares prediction equation for predicting sugar concentration in
moist tropical forest trees and shrubs from (NSC – 100).
j) Give an interpretation of the estimated intercept for moist tropical forest trees and
shrubs.
k) Give an interpretation of the estimated slope coefficient for moist tropical forest
trees and shrubs.
l) Is there a statistically significant linear relationship between (NSC – 100) and
sugar concentration for moist tropical forest trees and shrubs? Support your
answer statistically.
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2. Fit a multiple linear regression with sugar concentration as the response and (NSC –
100), an indicator variable for type of forest (Forest Indicator = 1 for moist tropical
forests, Forest Indicator = 0 for dry tropical forests) and a (NSC – 100) by Forest
Indicator interaction term. Turn off the Center Polynomials.
a) How much of the variability in sugar concentration is explained by the interaction
model?
b) What is the estimate of the error standard deviation? How does this compare to
your answers in 1 b) and 1 h)?
c) Give the least squares prediction equation for the interaction model.
d) Interpret each of the estimated parameters in the interaction model within the
context of the problem. Hint: It may be helpful to look at your equations and
interpretations in problem 1.
e) If tropical trees or shrubs have an NSC concentration of 100 mg/g, will the
population mean sugar concentration be different for dry and moist tropical
forests? Support your answer with the appropriate test of hypothesis or
confidence interval.
f) Are the sugar concentrations for tropical trees and shrubs from dry and moist
tropical forests changing at statistically different rates relative to the NSC
concentration? Support your answer with the appropriate test or confidence
interval.
g) Estimate the mean sugar concentration for trees and shrubs from dry tropical
forests that have NSC concentration of 100 mg/g. Include a 95% confidence
interval for the population mean sugar concentration.
h) Predict the sugar concentration for a tree or shrub from a dry tropical forest that
has an NSC concentration of 100 mg/g. Include a 95% prediction interval for the
the sugar concentration.
i) Describe the plot of residuals versus NSC. What does this indicate about the
predictions made using the interaction model?
j) Describe the distribution of residuals. Are the conditions of identically and
normally distributed errors satisfied? Explain briefly.
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