Lab 5

Simple Linear Regression

Author

YOUR NAME HERE

How to complete this lab

Fill in each ??? with the correct code. Once all placeholders are filled in, change completed: false to completed: true in the YAML header above and render to HTML. For your final submission, change format: html to format: pdf.

Overview

In this lab, you will practice fitting and interpreting a simple linear regression model using V-Dem democracy data. You will:

  1. Wrangle V-Dem data and visualize a bivariate relationship with a regression line
  2. Fit a simple linear regression model and interpret the output
  3. Apply what you learned to a research question of your own choosing

You are encouraged to have the lecture materials from Modules 9.2 and 10.1 open while completing this lab.

Getting Started

library(tidyverse)
library(vdemdata)
run <- isTRUE(params$completed)
Installing vdemdata locally

If you are working on your own computer and don’t have vdemdata installed, you can install it from GitHub. First install the pak package, then use it to install vdemdata:

install.packages("pak")
pak::pak("vdeminstitute/vdemdata")

The Data

You will work with cross-national data from the V-Dem project for the year 2019. The research question is: Are more democratic countries less corrupt?

The key variables are:

  • lib_dem — Liberal Democracy Index (0–1, higher = more democratic)
  • corruption — Political Corruption Index (0–1, higher = more corrupt)

Part 1: Wrangle and Visualize (40 points)

Step 1: Wrangle the data (15 pts)

Fill in the ??? to filter V-Dem to the year 2019 and select the relevant variables.

model_data <- vdem |>
  filter(year == ???) |>
  select(
    country = country_name,
    lib_dem = v2x_libdem,
    corruption = v2x_corr
  )

glimpse(model_data)

Question: How many rows does model_data have? What does each row represent?

YOUR ANSWER HERE

Step 2: Visualize the relationship (25 pts)

Create a scatter plot with lib_dem on the x-axis and corruption on the y-axis. Add a linear regression line using geom_smooth(). Include a title and axis labels, and use theme_bw().

# Write your plot code here

Question: Describe the relationship. Is it positive or negative? Does it look roughly linear?

YOUR ANSWER HERE

Part 2: Fit and Interpret the Model (60 points)

Step 1: Fit the model (10 pts)

Use lm() to fit a simple linear regression predicting corruption from lib_dem. Store the result in an object called model1 and view the output with summary().

model1 <- lm(??? ~ ???, data = model_data)

summary(model1)

Step 2: Write out the equation (10 pts)

Using the Estimate column from the output, write out the estimated regression equation below (round coefficients to two decimal places):

\[\widehat{Corruption}_i = a + b \times Democracy_i\]

YOUR EQUATION HERE

Step 3: Interpret the intercept (15 pts)

Question: What is the value of the intercept, and what does it represent in the context of this model?

YOUR ANSWER HERE

Step 4: Interpret the slope (15 pts)

Question: What is the value of the slope, and what does it tell us about the relationship between democracy and corruption? Be specific about direction and magnitude.

YOUR ANSWER HERE

Step 5: Statistical significance (10 pts)

Question: Is the slope statistically significant at the 0.05 level? How do you know from the summary() output?

YOUR ANSWER HERE

Part 3: Build Your Own Model (20 points)

Choose a different outcome variable and predictor from V-Dem that you find theoretically interesting. Wrangle the data, create a scatter plot with a regression line, fit the model, and interpret the slope and intercept.

# Write your code here

Question: What variables did you choose and why? Interpret the slope and intercept, and describe whether the results matched your expectations.

YOUR ANSWER HERE

Render as PDF and Submit Your Work (20 points)

  1. Replace “YOUR NAME HERE” at the top with your actual name
  2. Make sure all code chunks run without errors
  3. Click “Render” to create your PDF
  4. Submit the PDF to Blackboard

Hints

Only look at these if you’re stuck!

Hint 1 — Filtering to one year:

filter(year == 2019)

Hint 2 — Scatter plot with regression line:

ggplot(model_data, aes(x = lib_dem, y = corruption)) +
  geom_point() +
  geom_smooth(method = "lm", color = "#E48957", se = FALSE) +
  labs(
    title = "Democracy and Corruption, 2019",
    x = "Liberal Democracy Index",
    y = "Corruption Index"
  ) +
  theme_bw()

Hint 3 — Fitting a simple linear model:

model1 <- lm(corruption ~ lib_dem, data = model_data)
summary(model1)

Hint 4 — Reading the summary output:

The Estimate column gives the intercept and slope. The Pr(>|t|) column gives the p-value — values below 0.05 are statistically significant at the 5% level.