BTS 510 Lab 6

set.seed(12345)
library(tidyverse)
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library(Stat2Data)
theme_set(theme_classic(base_size = 16))

1 Learning objectives

  • Describe the logic of linear regression
  • Describe the assumptions of linear regression
  • Briefly present results of linear regression
  • Use a regression equation to summarize a model
  • Compare and contrast observed, predicted, and residual values

2 Data

  • ICU data from the Stat2Data package
    • ID: Patient ID code
    • Survive: 1 = patient survived to discharge or 0 = patient died
    • Age: Age (in years)
    • AgeGroup: 1 = young (under 50), 2 = middle (50-69), 3 = old (70+)
    • Sex: 1 = female or 0 = male
    • Infection: 1 = infection suspected or 0 = no infection
    • SysBP: Systolic blood pressure (in mm of Hg)
    • Pulse: Heart rate (beats per minute)
    • Emergency: 1 = emergency admission or 0 = elective admission

3 Tasks

  1. Does blood pressure differ between those with a suspected infection and those without? Fit a linear regression to answer this question.

  2. Write up the interpretation of the model, including:

  • Intercept value, test statistic, p-value
  • Intercept interpretation (in words)
  • Slope value, test statistic, p-value
  • Slope interpretation (in words)
  • R^2 value, test statistic, p-value
  • R^2 interpretation (in words)

  1. What is the predicted blood pressure for someone with a suspected infection? What is the predicted blood pressure for someone without a suspected infection?

  2. Calculate the predicted and residual values for each person and add them to the original dataset. Does it looks like the assumptions are satisfied? Make plots to help you decide:

  • Residual vs predictor
  • Q-Q plot of residuals
  • Histogram of residuals (all together and separately for the two groups)
  1. Does blood pressure differ between those with a suspected infection and those without? How? (Brief, simple words, no jargon, no statistics.)