AE 21: Inference for Logistic Regression Models

Important

  • Open RStudio and create a subfolder in your AE folder called “AE-21”.

  • Go to the Canvas and locate your AE-21 assignment to get started.

  • Upload the ae-21.qmd and framingham.csv files into the folder you just created. The .qmd and PDF responses are due in Canvas. You can check the due date on the Canvas assignment.

Packages

library(tidyverse)
library(broom)
library(ggformula)
library(mosaic)
library(knitr)

heart_disease <- read_csv("data/framingham.csv") |>
  select(TenYearCHD, totChol, currentSmoker, BMI, BPMeds, cigsPerDay, prevalentHyp, heartRate, diabetes) |>
  drop_na()

Data: Framingham study

This data set is from an ongoing cardiovascular study on residents of the town of Framingham, Massachusetts. We want to predict if a randomly selected adult is high risk for heart disease in the next 10 years.

Response variable

  • TenYearCHD:
    • 1: Patient developed heart disease within 10 years of exam
    • 0: Patient did not develop heart disease within 10 years of exam

What are my predictor variables?

Based on your group, use the following as your predictor variables.

  • Group 1:
    • totChol: total cholesterol (mg/dL)
    • currentSmoker: 1 if current smoker, 0 otherwise
  • Group 2:
    • BMI: patient’s body mass index
    • BPMeds: 1 if they are on blood pressure medication, 0 otherwise
  • Group 3:
    • cigsPerDay: number of cigarettes patient smokes per day
    • prevalentHyp: 1 if patient was hypertensive, 0 otherwise
  • Group 4
    • sysBP: systolic blood pressure (mmHg)
    • diabetes: 1 if patient has diabetes, 0 otherwise

Exercise 0

Fit two logistic regression models predicting TenYearCHD, one for each of your explanatory variables. Keep track of which one has a quantitative and which has a categorical predictor.

Exercise 1

For your quantitative predictor, conduct a hypothesis test to determine whether the slope of your variable is statistically significant. On the white board:

  1. Specify the null and alternative hypotheses.
  2. Compute the test statistic.
  3. Give the p-value.
  4. Interpret the result.

Exercise 2

For your quantitative variable. Construct a 99% confidence interval. Hint, you can use the conf.level argument in tidy to change the confidence level. On the white board:

  1. Interpret your confidence interval in log-odds.
  2. Interpret your confidence interval in odds.

Exercise 3

For your categorical predictor, conduct a hypothesis test and construct 95% confidence interval for your \(\beta_1\). Interpret these in context and be prepared to discuss with the class. Note that you need not write down the entire hypothesis testing framework.

Exercise 4

Why do you think it doesn’t quite make sense to talk about prediction intervals or confidence intervals in the context of a logistic regression model?

Submission

Important

To submit the AE:

  • Render the document to produce the PDF with all of your work from today’s class.
  • Upload your QMD and PDF files to the Canvas assignment.