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Question 2
The data for this question comprises measurements on breeding pairs of land-bird species collected
from 16 islands around Britain over the course of several decades available in a .csv le, bird. For
each species, the data set contains an average time of extinctions, extinct, on those islands where
the species appeared. (This is actually the reciprocal of the average of 1/T where T is the length of
time the species remained on the island and 1/T is taken to be zero if the species did not become
extinct on the island); the average number of nesting pairs per year, over all islands where the species
appeared (nest.pair); the size (size) of the species, (S = Small, L = Large); and the migratory
status (mig.status) of the species, (R = Resident, M = Migrant). It is expected that species
with large numbers of nesting pairs will tend to remain longer before becoming extinct. Of particular
interest is whether, after accounting for the number of nesting pairs, size or migratory status has any
e ect.
(a) Fit a multiple linear regression (MLR) model with extinct as the response variable and all
other covariates as predictors. Is the regression model signi cant? Interpret the coecients
for the categorical variables in this model. Does the coecient support the expectations that
large number of nesting pairs tend to delay extinction?
(b) As the question indicates, of particular interest is whether, after accounting for the number
of nesting pairs, size or migratory status has any effect. Conduct a formal test of the
hypothesis that βSize= βMigStatus= 0 using an appropriate anova table. Evaluate the Fstatistic
and the corresponding p-value.
(c) The Red-crested Periwinkle is a small, migratory species of bird, while the Great Plover isa
large, resident species of bird. Assuming that the number of nesting pairs is thesame for each
species over the period, based on the model in part (a), what would you predict the di
erence in extinction times to be for these two species?
(d) A noted theory suggests that Size and Migratory Status should contribute equally to the
extinction time. Test whether the coecients of size and mig.status are the same.
Construct an appropriate model to test this hypothesis.
(e) Produce the appropriate diagnostic plots for the model tted in part (a) and as-sess the
model assumptions. Produce the relevant in
uence diagnostics for this model. Which data
pointsappear to bein
uential in theanalysis,and in what sense would you consider them in
-
uential? Also, do any points appear to be outliers? If so, to which species do these points
correspond?
(f) Two transformations are suggested for the response variable, log(extinct) and 1/
extinct. Investigatewhether using thesetransformationsimproves on themodel t. Comment
on theassumptions of MLR forthesemodelsas compared to your originalmodel. Which
of three models would you choose based on your analysis?
Assignment 2 - Sem 1, 2019 Page 3 of 3