## Description

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

links.

(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