Exercise: Predicting Firm Exit with Logistic Regression

Practice logistic regression end-to-end: fit a model for binary firm exit, extend it with additional predictors, interpret odds ratios, compute scenario-based predicted probabilities, and communicate findings with inline R code.

TipBefore you start

This exercise accompanies the Logistic Regression for Binary Outcomes tutorial. Work through that page first.

Data: bisnode-firms.csv — ~17,500 Hungarian manufacturing and services firms. Download from gabors-data-analysis.com and place in a data/ subfolder.

Business question: Can we predict which firms are likely to exit the market in the next year?

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1 Setup

library(tidyverse)
library(modelsummary)
library(marginaleffects)
library(broom)

firms <- read_csv("data/bisnode-firms.csv")

Take two minutes to explore the data:

glimpse(firms)

Rows: 17,506
Columns: 11
$ comp_id       <dbl> 1002029, 1011889, 1014183, 1018301, 1022796, 1035705, 10…
$ exit          <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 1, 0, 0, 0,…
$ sales_log     <dbl> 13.943477, 12.980031, 11.773208, 8.813174, 10.169549, 10…
$ employees_log <dbl> -0.78015860, 0.48317409, -0.33508429, -1.87877086, -2.48…
$ profit_margin <dbl> 0.008554417, 0.223101892, -0.018128871, -0.164738285, -0…
$ age           <dbl> 6, 20, 11, 8, 11, 1, 14, 5, 2, 4, 2, 1, 2, 4, 16, 1, 23,…
$ liquidity     <dbl> 1.69277357, 8.46944789, 24.16025018, 3.05624997, 0.90785…
$ foreign       <dbl> 0, 0, 0, 0, 0, 0, 1, 0, 0, 0, 0, 0, 0, 0, 0, 1, 0, 0, 0,…
$ female_ceo    <dbl> 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 1, 1, 0, 0, 0, 0, 0, 1,…
$ industry      <dbl> 27, 55, 55, 56, 56, 56, 29, 56, 56, 27, 41, 55, 56, 28, …
$ urban         <dbl> 0, 0, 0, 0, 1, 0, 0, 0, 1, 0, 1, 1, 1, 0, 1, 0, 0, 0, 0,…

Before coding: What does one row represent? What does exit = 1 mean?

Your answer:

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2 Task 1: Fit a Logistic Regression Model

Fit a logistic regression model that predicts firm exit using:

• sales_log (log of sales revenue)
• profit_margin (profit as a share of sales)
• employees_log (log of number of employees)
• age (firm age in years)

Call your model model_base.

# model_base <- ___

# summary(model_base)

1a. Which predictors are statistically significant at the 5% level?

Your answer:

1b. Based on the signs of the coefficients, which factors increase and which decrease the probability of exit? Does this make economic sense?

Your answer:

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3 Task 2: Extend Your Model

Add at least two more predictors to your model. Use subject-matter intuition: which firm characteristics might predict exit?

# names(firms)   # explore available variables

# model_ext <- ___

Compare your two models with modelsummary():

# modelsummary(list("Base" = model_base, "Extended" = model_ext), ...)

2a. Did adding the new predictors improve model fit? Use AIC to compare (lower is better).

Your answer:

2b. Did any coefficients shift notably when you added the new variables? What might that indicate?

Your answer:

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4 Task 3: Interpret Coefficients as Odds Ratios

Compute and display the odds ratios with 95% confidence intervals for your extended model:

# exp(coef(model_ext))
# exp(confint(model_ext))

Task 3: Choose one predictor and write a complete interpretation using this template:

“A one-unit increase in [variable] is associated with a multiplication of the odds of firm exit by [odds ratio]. This means the odds of exit [increase/decrease] by [X]%. This effect is [statistically significant / not significant] at the 5% level.”

Your answer:

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5 Task 4: Predicted Probabilities for Two Firm Profiles

Define two contrasting firm profiles and compute the predicted probability of exit for each:

# scenarios <- tibble(
#   label         = c("Profile A: ___", "Profile B: ___"),
#   sales_log     = c(___, ___),
#   employees_log = c(___, ___),
#   profit_margin = c(___, ___),
#   age           = c(___, ___)
#   # add predictors you included in model_ext
# )

# scenarios |>
#   mutate(pred_prob = predict(model_ext, newdata = scenarios, type = "response"))

Task 4: Describe your two profiles and explain what story the predicted probabilities tell.

Your answer:

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6 Task 5: Communicate a Finding with Inline R Code

Write a short paragraph (3–5 sentences) summarising one key finding. Embed at least two numbers as inline R code (not typed manually).

Your paragraph:

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7 Bonus: Average Marginal Effects

Compare the AME for profit_margin from logistic regression to the LPM coefficient for the same variable. Are they similar? What does this tell you about when the LPM might be acceptable?

# avg_slopes(model_ext)
# lpm <- lm(exit ~ sales_log + profit_margin + employees_log + age, data = firms)

Your answer: