The involves a dataset, PimaDiabetes.csv, derived from one originally collected by the USA’s National Institute of Diabetes and Digestive and Kidney Diseases1. It lists various diagnostic measures recorded from 750 women along with a 0/1 variable, Outcome, that indicates whether the person eventually tested positive for diabetes. Table 1 shows the first few rows of the dataset while the diagnostic measures are explained below.

Pregnancies: number of times the woman has been pregnant

Glucose: plasma glucose concentration (mg/dl) at 2 hours in an oral glucose tolerance test (OGTT)

Blood Pressure: Diastolic blood pressure (mm Hg)

Skin Thickness: Triceps skin fold thickness (mm)

Serum Insulin: insulin concentration2 (μ U/ml) at 2 hours in an OGTT

BMI: body mass index (weight in kg)/(height in m)2

Diabete Pedigree: a numerical score designed to measure the genetic influence of both the woman’s diabetic and her non‑diabetic relatives on diabetes risk: higher scores mean higher risk. Youcan read more about this in Smith, Everhart, Dickson, Knowler, and Johannes (1988).

Age: in years

Outcome: 1 if the woman eventually tested positive for diabetes, zero otherwise

1. Write a brief description of the data, including its origin and quality issues. You should imagine you are writing for a group who have no idea what this dataset is about.

2. Do an exploratory data analysis.

3. Add a column, ThreeOrMoreKids, to the dataset that answers the question “Does the woman have 3 or more children?”, then fit an appropriate regression model to predict whether a woman will develop diabetes using ThreeOrMoreKids as a single predictor. With the help of the fitted model, answer the following questions (show your calculations, either by hand or with help of R or Python): • What is the probability that you get diabetes, given that you have two or fewer children? • What is the probability that you get diabetes, given that you have three or more children?

4. Using the data in PimaDiabetes.csv, fit appropriate regression models and use them to determine how likely the women whose data are listed in Table 2 are to develop diabetes. You are free to choose which explanatory variables to inclue in your model and may, if you like, compare several models, but make sure that you clearly state the final model chosen and the reasons behind this choice. With the help of your chosen model, interpret the results in terms of probability of developing diabetes (as you did for the model based on ThreeOrMoreKids).

5. Include R or Python code used to produce the analysis.