ISC4241 Assignment 5 Solution

The data set used in this activity is “HeartDisease.txt”. The data set used in this study is from South African Heart Disease Data (http://www-stat.stanford.edu/~tibs/ElemStatLearn/data.html), a subset `of the Coronary Risk-Factor Study (CORIS) of the Western Cape, South African. The aim of this study was to establish the intensity of ischemic heart disease risk factors in the highincidence region. (Note: the target variable for this study is “chd”.

Problem 1 Programming and Reporting (20 Points)
PART I Programming (10 Points)
1. Read the data into your software system
2. Examine univariate statistics for the following variables: sbp, tobacco, ldl, adiposity, typea, obesity, alcohol, and age. (not including the target variable)
3. Produce histogram of each of the following variables with imposing normal curve: sbp, tobacco, ldl, adiposity, typea, obesity, alcohol, and age.
4. Produce quantile plot of each of the following variables: sbp, tobacco, ldl, adiposity, typea, obesity, alcohol, and age.
5. Build a logistic regression model with all predictors.
6. Perform power transformation on the following variables: sbp (power = -2), tobacco (power = 0.4), ldl (power = 0.1), obesity (power = -0.4), and alcohol (power = 0.4).
7. Produce histogram of each of the following transformed variables with imposing normal curve: sbp, tobacco, ldl, obesity, and alcohol.
8. Produce quantile plot of each of the following transformed variables: sbp, tobacco, ldl, obesity, and alcohol.
9. Build a logistic regression model with all predictors (transformed and three remaining original variables do not perform any transformation).
10. Build another logistic regression model with all predictors as in Part 9 except using significant predictors only.
PART II Reporting
1. After completion of this activity, complete the following table. (3 Points)
Variable Name Mean Median Skewness
sbp
tobacco
ldl
adiposity
typea
obesity
alcohol
age

2. Display the histogram and quantile plot of “tobacco”.
3. Display the histogram and quantile plot of “alcohol”.
4. Complete the following table. (3 Points)
Variable Name Mean Median Skewness
Sbp (Power=-2)
Tobacco (Power=0.4)
Ldl (Power=0.1)
obesity (power = -0.4)
alcohol (Power=0.4)

5. Display the histogram and quantile plot of “tobacco” after power transformation.
6. Display the histogram and quantile plot of “alcohol” after power transformation.
7. Find the 95% confidence interval on the likelihood of heart disease if one more kilogram of tobacco consumed using the first model.
8. Find the 95% confidence interval on the likelihood of heart disease if one more kilogram of alcohol consumed using the first model.
9. Which model perform better based on the c-statistics?

Problem #2 (5 Points) Suppose that we collect data from a group of students in statistics with variables “Hours of Study” (𝑋1) and “Undergraduate GPA” (𝑋2), and “Receiving A as Final Grade” (𝑌). We fit a logistic regression model with the following estimates: 𝛽̂0 = −4, 𝛽̂1 =
0.06, 𝑎𝑛𝑑 𝛽̂2 = 0.5.
a) Estimate the probability of a student who spent 10 hours per week with 3.5 undergraduate GPA.
b) How many hours would the student in part (a) need to study to have 80% or higher chance of getting A in this class?

Problem #3 (5 Points)
a) What is the fraction of people with an odd of 0.3 of defaulting on their credit card payment?
b) Suppose that John has 10% chance default in his credit card payment. What is the odd that John will default?