hw2

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Stat 960:587 Homework No. 2
Due 3/20/2019
Programming: R or Python
Problem 1. Car purchase. A marketing research firm was engaged by an
automobile manufacturer to conduct a pilot study to examine the feasibility of using
logistic regression for ascertaining the likelihood that a family will purchase a new
car during the next year. A random sample of 33 suburban families was selected.
Data on annual family income (X1, in thousand dollars) and the current age of the
oldest family automobile (X2, in years) were obtained. A follow-up interview
conducted 12 months later was used to determine whether the family actually
purchased a new car (Y = 1) or did not purchase a new car (Y = 0) during the year.
You can find all the data in the CarPurchaseData.txt attachment.
i
Xi1
Xi2
Yj
1
32
3
0
2
45
2
0
3
60
2
1
...
...
...
...
31
21
3
0
32
32
5
1
33
17
1
0
Multiple logistic regression model with two predictor variables in first-order terms
is assumed to be appropriate.
a. Find the maximum likelihood estimates of βo, β1, and β2. State the fitted response
function.
b. Obtain exp(b1) and exp(b2) and interpret these numbers.
c. What is the estimated probability that a family with annual income of $50
thousand and an oldest car of 3 years will purchase a new car next year?
Problem 2. Knight & Skagen (1988) collected the data shown in the table during a
field study on the foraging behavior of wintering Bald Eagles in Washington State,
USA. The data concern 160 attempts by one (pirating) Bald Eagle to steal a chum
salmon from another (feeding) Bald Eagle. The abbreviations used are:
Number of
successful
attempts
17
29
17
20
1
15
0
1
L = large S = small A = adult I = immature
Total number
of attempts
24
29
27
20
12
16
28
4
Size of
pirating eagle
L
L
L
L
S
S
S
S
Age of pirating
eagle
A
A
I
I
A
A
I
I
Size of feeding
eagle
L
S
L
S
L
S
L
S
Report on factors that explain the success of the pirating attempt and give a
prediction formula for the probability of success
Problem 3. The following data are part of a survey by Dr Mutch of low-weight
births in Scotland between 1981 and 1988. The table refers to 661 children with
birth weights between 650g and 1749g all of whom survived for at least one year.
The variables of interest are:
Cardiac: mild heart problems of the mother during pregnancy;
Comps: gynaecological problems during pregnancy;
Smoking: mother smoked at least one cigarette per day during the first 6 months of
pregnancy;
BW: was the birth weight less than 1250g?
Cardiac
Comps
Smoking
BW
Analyse this table.
Yes
No
Yes
Yes
No
Yes
No Yes No
10
25
12
15
7
5
22
19
Yes
Yes No
18
12
10
12
No
No
Yes No
42
45
202 205
Problem 4. Refer to Car purchase,
a. To assess the appropriateness of the logistic regression function, form three
groups of 11 cases each according to their fitted logit values πˆ ' . Plot the estimated
proportions pj against the midpoints of the πˆ ' intervals. Is the plot consistent with a
response function of monotonic sigmoidal shape? Explain.
b. Obtain the deviance residuals and present them in an index plot. Do there appear
to be any outlying cases?
c. Construct a half-normal probability plot of the absolute deviance residuals. Do
any cases here appear to be outlying?
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