Homework 7: Diabetes
36-402, Advanced Data Analysis
Due at the start of class, 22 March 2011
A classic data set for classification problems, logistic regression and related
methods comes from a study of the correlates of diabetes among the Pima
Indians of Arizona, collected as part of a long-term study to understand why
the Pima, like many other Native American groups, suffer from a much higher
rate of diabetes than other populations in the US. (For background on the
study, and the issue, see http://diabetes.niddk.nih.gov/dm/pubs/pima/.)
Our version of the data is the data set pima in the package faraway.1It contains
information of 768 adult Pima women, some but not all of whom have diabetes.
See help(pima) for a description of the variables. Note that the column named
diabetes indicates how much of a history of diabetes there was in the woman’s
family; it is the last column, test, which indicates whether the or not the woman
herself is diabetic.
1. (10 points) Make graphic and numerical summaries of the data. If there
are any obvious irregularities in the data, describe them, say why you
think they are irregularities, and remove them as appropriate.
2. (20 points) Fit a logistic regression model to predict diabetes, using all
the other variables as inputs. What are the estimated coefficients?
3. (10 points) What is the probability of having diabetes for a woman who
has been pregnant twice, has a glucose concentration of 99, a diastolic
pressure of 64, 22 mm of tricep thickness, an insulin level of 76, a BMI of
26, a diabetes “pedigree function” of 0.25, and is 30 years old. Give a 95%
confidence interval for this prediction, assuming the model is correctly
specified.
4. (10 points) How do the odds of having diabetes change for a woman who
moves from the third quartile of the BMI distribution to the first quar-
tile, with all else held constant? Give a 95% confidence interval for the
difference in odds, assuming the model is correct specified.
5. (20 points) Do women with diabetes have higher diastolic blood pressure
than women without diabetes? Is the blood pressure coefficient signifi-
cant in your model? Explain why the answers to these two questions are
actually compatible.
1This homework is in fact based on problem 3 in chapter 2 of Faraway’s textbook.
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