This homework is due on Apr 11, 2024 at 11:00pm. Please submit as a pdf file on Canvas.

For both problems in this homework, we will work with the heart_disease_data dataset, which is a simplified and recoded version of a dataset available from kaggle. You can read about the original dataset here: https://www.kaggle.com/datasets/kamilpytlak/personal-key-indicators-of-heart-disease?resource=download

The heart_disease_data dataset contains 9 variables: HeartDisease (whether or not the participant has heart disease), BMI (body mass index), PhysicalHealth (how many days a month was their physical health not good), MentalHealth (how many days a month was their mental health not good), ApproximateAge (participants age), SleepTime (how many hours of sleep do they get in a 24-hour period), Smoking (1-smoker, 0-nonsmoker), AlcoholDrinking (1-drinks alcohol, 0-does not drink), PhysicalActivity (1-did physical activity or exercise during the past 30 days, 0-hardly any physical activity). Compared to the original dataset, the columns ApproximateAge, Smoking, AlcoholDrinking, and PhysicalActivity have been converted into numeric columns so they can be included in a PCA.

Note: This homework is about the contents of the plots. Don’t worry about styling. It’s OK to use the default theme and plot labeling.

heart_data <- read_csv("https://wilkelab.org/SDS375/datasets/heart_disease_data.csv")

Problem 1: (10 pts)

Perform a PCA of the numerical colums of the heart_disease_data dataset. Then make two plots, a rotation plot of components 1 and 2 and a plot of the eigenvalues, showing the amount of variance explained by the various components.

# your code here
# your code here

Problem 2: (10 pts) Make a scatter plot of PC 2 versus PC 1 and color by heart disease status. Then use the rotation plot from Problem 1 to describe the variables/factors by which we can separate the study participants with heart disease from the study participants without heart disease.

# your code here