Homework 3

Linear regression

  • Due Sunday, June 29 by end of day (midnight)

  • Complete the assignment in a Quarto (.qmd) document and render it to HTML and PDF. Email all 3 files (.qmd, .html, .pdf) to Stefany, Yujie, and Michael.

    • Remember to include embed-resources: true in the html options. If you don’t, we won’t see any of your figures when you send the files.

Data

  • Pulse dataset from the Stat2Data package
    • A dataset with 232 observations on the following 7 variables. Active: Pulse rate (beats per minute) after exercise Rest: Resting pulse rate (beats per minute) Smoke: 1=smoker or 0=nonsmoker Sex: 1=female or 0=male Exercise: Typical hours of exercise (per week) Hgt: Height (in inches) Wgt: Weight (in pounds)

Research question

How do patient sex and smoking status predict active pulse rate?

Tasks

  1. Conduct three linear regression models to address the above research question.
  • Model 1: Patient sex predicts active pulse rate
  • Model 2: Patient smoking status predicts active pulse rate
  • Model 3: Patient sex and smoking status predict active pulse rate
  1. Which is the best model?
  • Use the \(F\)-test for \(R^2_{change}\) and the AIC values to help you decide. Report the tests and values that you used to decide this.
  1. Report the results of the best model, including:
  • Intercept value, test statistic, \(p\)-value, interpretation (in words)
  • Slope value(s), test statistic(s), \(p\)-value(s), interpretation(s) (in words)
  • \(R^2\) value, test statistic, \(p\)-value, interpretation (in words)

  1. Based on model 3, what are the predicted active pulse rates for the 4 combinations of sex and smoking status? (i.e., female non-smoker, male non-smoker, female smoker, male smoker)

  2. Using the predicted and residual values, assess whether the assumptions are met for model 3. Include the plots and describe your conclusions based on them.

  3. In plain language, answer the research question: How do patient sex and smoking status predict active pulse rate? (This should not be lengthy – just a couple sentences.)