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# P8131 Homework 2 solved

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1. (40%) The table below gives the data collected from a bioassay study in which
X variable (treated as continuous variable) is the concentration level. At each of
five different dose levels (0-4), 30 animals are tested and the number of dying are
recorded.
Dose (X) 0 1 2 3 4
Number of dying 2 8 15 23 27

Fit the model g(P(dying)) = α+βX, with logit, probit, and complementary log-log
(a) Fill out the table and give comments.
Model Estimate of β CI for β Deviance pˆ(dying|x = 0.01)
logit
probit
c-log-log

(b) Suppose that the dose level is in natural logarithm scale, estimate LD50 with
90% confidence interval based on the three models.
2. (60%) The table below contains the enrollment data of some MPH program in a
year
• Amount: one-time two-year scholarship
• Offer: the number of offers made with the corresponding scholarship
• Enrolls: the number of offer accepted
1

Amount (in thousand dollars) Offers Enrolls
10 4 0
15 6 2
20 10 4
25 12 2
30 39 12
35 36 14
40 22 10
45 14 7
50 10 5
55 12 5
60 8 3
65 9 5
70 3 2
75 1 0
80 5 4
85 2 2
90 1 1

Please analyze the data using a logistic regression and answer the following questions:
(a) How does the model fit the data?
(b) How do you interpret the relationship between the scholarship amount and
enrollment rate? What is 95% CI?

(c) How much scholarship should we provide to get 40% yield rate (the percentage
of admitted students who enroll?) What is the 95% CI?
2