Take-home task 1: what you did

Dataset: CPS 2014 — market research analysts and marketing specialists

What you built:

• Model 1: earnings ~ age (linear)
• Model 2: earnings ~ age + age² (quadratic — better residual pattern)
• Model 3: earnings ~ age + age² + hours + college (with controls)

Common issues: interpretation

Too vague: “The college coefficient is 128.4.”

Two new tools for Session 2

From Task 1 onwards you explored results using raw R output.

Session 2 introduces two tools that turn raw output into presentation-ready tables:

Raw output using summary()

summary(m1)

Call:
lm(formula = earnwke ~ age, data = cps)

Residuals:
    Min      1Q  Median      3Q     Max 
-1317.7  -465.2  -107.9   289.4  1772.0 

Coefficients:
            Estimate Std. Error t value Pr(>|t|)    
(Intercept)  724.712    151.674   4.778 3.02e-06 ***
age           14.365      3.728   3.854 0.000148 ***
---
Signif. codes:  0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1

Residual standard error: 660.1 on 250 degrees of freedom
Multiple R-squared:  0.05608,   Adjusted R-squared:  0.0523 
F-statistic: 14.85 on 1 and 250 DF,  p-value: 0.0001479

The answer to Reflection Question 1

“Your analysis left out one important individual characteristic that is systematically linked to earnings. Which variable is this?”

tidy(cor.test(cps$female, cps$earnwke)) |>
  select(estimate, p.value, conf.low, conf.high) |>
  mutate(across(everything(), \(x) round(x, 3))) |> 
  flextable() |> 
  theme_vanilla()

What is a categorical variable?

A variable that takes a finite set of named values — not a continuous scale.

How R handles categories

R picks one category as the reference group and creates one binary (0/1) indicator for each remaining category.

Example: Gender (reference = Male)

cps <- cps |> mutate(female = ifelse(sex == 2, 1, 0))
# OR: use factor(sex) and let R create the dummies automatically

Interpreting a dummy coefficient

Model: earnwke ~ age + uhours + female

Where do dummy coefficients come from?

In a simple regression of earnings on gender only, the coefficient equals the raw mean difference:

cps |>
  group_by(female) |>
  summarise(mean_earn = round(mean(earnwke), 1)) |>
  mutate(diff_vs_male = round(mean_earn - mean_earn[female == 0], 1)) |> 
  flextable() |> 
  theme_vanilla()

coef(lm(earnwke ~ female, data = cps))["female"] |> round(1)

female 
-218.4 

Multi-category variables

What if we want education as three levels, not a binary college/no-college split?

• Pick a reference category (e.g. “No degree”)
• R creates k − 1 dummy variables for k categories
• Each coefficient = difference from the reference group

cps |>
  group_by(edu_cat) |>
  summarise(mean_earn = round(mean(earnwke), 1)) |>
  mutate(vs_no_degree = round(mean_earn - mean_earn[edu_cat == "No degree"], 1)) |>
  flextable() |>
  theme_vanilla() |> 
  autofit()

Why the reference category matters

Same model, different reference — different numbers, same underlying story.

• Reference = No degree: Bachelor +$80, Graduate +$180
• Reference = Bachelor: No degree −$80, Graduate +$100
• Reference = Graduate: No degree −$180, Bachelor −$100

factor(c("Graduate", "No degree", "Bachelor"))
# Levels: Bachelor's  Graduate  No degree   ← Bachelor is reference (B < G < N)

factor(c("Graduate", "No degree", "Bachelor's"), levels = c("No degree", "Bachelor", "Graduate"))
# Levels: Bachelor's  Graduate  No degree   ← No degree is reference (N < B < G)

factor(edu, levels = c("No degree", "Bachelor's", "Graduate"))
# Now "No degree" is the reference
relevel(factor(edu), ref = "No degree")  # same result

Interaction terms: motivation

A regression without interactions assumes: The effect of age on earnings is the same for men and women.

The marginal effect of age

With interactions, “the effect of age” depends on the group.

b <- coef(lm(earnwke ~ age * female, data = cps))

• Age slope for men: round(b["age"], 2) = 18.54
• Age slope for women: round(b["age"] + b["age:female"], 2) = 11.31
• Difference: round(b["age:female"], 2) = -7.23

Live coding demo

We return to the CPS data and extend the take-home analysis:

1. Add female back from the raw CPS file
2. Fit Model 3 from the take-home, now including gender
3. Recode grade92 from binary to three education categories
4. Visualise: do male and female age-earnings profiles look parallel?
5. Add an age × female interaction
6. Compare all models in one clean modelsummary table

Exercise: hotel prices in Vienna

Business question: What drives hotel prices — and does the price penalty for being far from the city centre differ between budget and luxury hotels?

Dataset: 428 hotels in Vienna (Békés & Kézdi 2021) Download from OSF: osf.io/4e6d8

Your tasks:

1. Explore the data — understand what one observation represents
2. Model price as a function of distance and stars (numeric, then as a factor)
3. Add an interaction: does the distance effect vary by star category?
4. Present all models in a clean modelsummary table
5. Write a plain-language paragraph for a non-technical manager

Take-Home Task 2

Assigned today — due 30 April 2026, 08:00

Dataset: Hotels Europe — prices and features across 46 European cities (Békés & Kézdi 2021)

• Build four regression models of increasing complexity (distance → city type → stars → interaction)
• Use modelsummary for regression tables and flextable for descriptive statistics
• Visualise the price–distance relationship before interpreting the model
• Reflect critically on what your model leaves out

See you on 30 April

Next session: Thu, 30 April — Modelling binary and categorical outcomes

Questions during the break? GitHub Discussions

Task 2 deadline: 29 April 2026, 23:59