Homework: Statistical Modeling and Interpretation

Due Thursday, November 12, 2026, 11:59 pm (Pacific)

Author

Your Name

Published

04 November 2026

Instructions

This homework focuses on interpretation and presentation of statistical results. You will apply linear regression (with categorical predictors and interactions) and logistic regression to the Bechdel Test movie dataset.

Total Points: 100

Linear Regression (30 points)
Logistic Regression (30 points)
Comprehensive Analysis (25 points)
Same Data, Different Goals (15 points)

Submission Requirements:

Self-contained HTML document with code hidden (use code-fold: true)
Focus on clear interpretation of results, not code mechanics
Please DO NOT use any LLMs in writing your answers. No tool is required, and no one is advantaged by paying for one (see the syllabus AI Policy).
Where AI would fail here: AI often gives textbook-generic interpretations that misstate coefficient meanings (for example, treating log-odds as probabilities), claim assumptions are satisfied without looking at your diagnostic plots, and invent p-values or effect sizes. Your interpretation of your output is what is graded.
Homework check: I may ask you to briefly explain one of your solutions in the Wednesday section (random sample, about 5 minutes).
Include well-formatted tables and figures
Write results as if for a technical report

Background: The Bechdel Test

The Bechdel Test measures female representation in films. A movie passes if it has:

At least two named women
Who talk to each other
About something besides a man

In the data, clean_test records where each movie stops: nowomen (fewer than two named women), notalk (they don’t talk to each other), men (they only talk about a man), dubious (disputed), or ok (passes). The variable binary is PASS only for ok; everything else, including dubious, is FAIL.

The Goal of This Homework: Description

As we saw in Week 5, the same model can be used to describe, to infer or to predict, and the goal changes what you report and what you check. In this homework the goal is description.

The data are 1794 movies released between 1970 and 2013 that FiveThirtyEight could match between BechdelTest.com (ratings submitted by volunteers) and The-Numbers.com (budget and revenue). This is not a random sample of all movies: it leans toward movies that are popular enough for someone to rate them and for their finances to be public.

So every research question below asks: what patterns are there in these movies? Some movies have missing values, so each model will use fewer than 1794; report how many movies each model uses. In your answers:

Describe associations in these movies. Write “among these movies, …” and not “movies in general …”
Do not make causal claims. A coefficient for budget is not “the effect of spending one more dollar”
Report effect sizes (coefficients, odds ratios, fitted values) and show them in figures. When p-values and confidence intervals are requested, treat them as a rough guide to how precisely these data pin down a pattern, not as a claim about a population
Check the assumptions that matter for description: is a straight line (or the model you chose) an honest summary of the pattern?

Recommended: Use the PCS Framework

We recommend framing your analysis with Yu & Barter’s PCS framework from Week 3 (Veridical Data Science, Ch. 1-2): is each pattern you describe real, or a product of noise and your own choices?

Predictability: Does the pattern reemerge in data you didn’t use to find it, for example in a held-out half of the movies? Is it consistent with what you know about the movie industry?
Computability: Every number in your report comes from code in the document. Every judgment call (log scale or not, units, rows dropped, how you treat dubious) is a line of code with a comment saying why. Use set.seed() before anything random.
Stability: Does your conclusion survive reasonable alternative choices? For example: raw vs. log scale, dropping the few biggest blockbusters, or treating dubious movies as missing instead of FAIL.

You don’t need to run every check for every question. Pick the ones that matter most for your conclusions and mention them briefly in your write-up.

Load the Data

Show code

library(tidyverse)
library(broom)
library(knitr)

# Load the movies dataset (1970-2013)
# Missing values are coded as "#N/A" or "N/A" in the file
movies <- readr::read_csv('https://raw.githubusercontent.com/rfordatascience/tidytuesday/master/data/2021/2021-03-09/movies.csv',
                          na = c("", "NA", "#N/A", "N/A"))

# Preview
glimpse(movies)

Rows: 1,794
Columns: 34
$ year          <dbl> 2013, 2012, 2013, 2013, 2013, 2013, 2013, 2013, 2013, 20…
$ imdb          <chr> "tt1711425", "tt1343727", "tt2024544", "tt1272878", "tt0…
$ title         <chr> "21 &amp; Over", "Dredd 3D", "12 Years a Slave", "2 Guns…
$ test          <chr> "notalk", "ok-disagree", "notalk-disagree", "notalk", "m…
$ clean_test    <chr> "notalk", "ok", "notalk", "notalk", "men", "men", "notal…
$ binary        <chr> "FAIL", "PASS", "FAIL", "FAIL", "FAIL", "FAIL", "FAIL", …
$ budget        <dbl> 1.30e+07, 4.50e+07, 2.00e+07, 6.10e+07, 4.00e+07, 2.25e+…
$ domgross      <dbl> 25682380, 13414714, 53107035, 75612460, 95020213, 383624…
$ intgross      <dbl> 42195766, 40868994, 158607035, 132493015, 95020213, 1458…
$ code          <chr> "2013FAIL", "2012PASS", "2013FAIL", "2013FAIL", "2013FAI…
$ budget_2013   <dbl> 13000000, 45658735, 20000000, 61000000, 40000000, 225000…
$ domgross_2013 <dbl> 25682380, 13611086, 53107035, 75612460, 95020213, 383624…
$ intgross_2013 <dbl> 42195766, 41467257, 158607035, 132493015, 95020213, 1458…
$ period_code   <dbl> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,…
$ decade_code   <dbl> 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1, 1,…
$ imdb_id       <chr> "1711425", "1343727", "2024544", "1272878", "0453562", "…
$ plot          <chr> NA, NA, "In the antebellum United States, Solomon Northu…
$ rated         <chr> NA, NA, "R", "R", "PG-13", "PG-13", "R", "R", "PG-13", "…
$ response      <lgl> NA, NA, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, TRUE, …
$ language      <chr> NA, NA, "English", "English, Spanish", "English", "Engli…
$ country       <chr> NA, NA, "USA, UK", "USA", "USA", "USA", "USA", "UK", "US…
$ writer        <chr> NA, NA, "John Ridley (screenplay), Solomon Northup (base…
$ metascore     <dbl> NA, NA, 97, 55, 62, 29, 28, 55, 48, 33, 90, 58, 52, 78, …
$ imdb_rating   <dbl> NA, NA, 8.3, 6.8, 7.6, 6.6, 5.4, 7.8, 5.7, 5.0, 7.5, 7.4…
$ director      <chr> NA, NA, "Steve McQueen", "Baltasar Kormákur", "Brian Hel…
$ released      <chr> NA, NA, "08 Nov 2013", "02 Aug 2013", "12 Apr 2013", "25…
$ actors        <chr> NA, NA, "Chiwetel Ejiofor, Dwight Henry, Dickie Gravois,…
$ genre         <chr> NA, NA, "Biography, Drama, History", "Action, Comedy, Cr…
$ awards        <chr> NA, NA, "Won 3 Oscars. Another 131 wins & 137 nomination…
$ runtime       <chr> NA, NA, "134 min", "109 min", "128 min", "118 min", "98 …
$ type          <chr> NA, NA, "movie", "movie", "movie", "movie", "movie", "mo…
$ poster        <chr> NA, NA, "http://ia.media-imdb.com/images/M/MV5BMjExMTEzO…
$ imdb_votes    <dbl> NA, NA, 143446, 87301, 43608, 25735, 123837, 85871, 1897…
$ error         <lgl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, …

Key Variables:

binary: Pass/Fail the Bechdel test
clean_test: Where the movie stops on the test (nowomen, notalk, men, dubious, ok)
budget_2013: Movie budget (adjusted to 2013 dollars)
domgross_2013: Domestic gross revenue (2013 dollars)
intgross_2013: International gross revenue (2013 dollars)
year: Release year
imdb_rating: IMDB rating (1-10 scale)
metascore: Metacritic score (0-100)
rated: MPAA rating (G, PG, PG-13, R, etc.)

Budgets and revenues are in dollars. Consider dividing them by 1,000,000 so that coefficients are per million dollars and easier to read.

Question 1: Linear Regression (30 points)

Research Question (descriptive): Among these movies, how does domestic gross revenue change with budget? Is that pattern different for movies that pass vs. fail the Bechdel test?

You are describing how revenue and budget move together in this dataset, and whether the line looks different for the two groups. You are not estimating how much extra revenue a studio would get by spending more, and not predicting the revenue of future movies.

Part A: Model Fitting (10 points)

Fit a linear regression model relating domestic gross revenue to budget, Bechdel test result (binary), and their interaction. Include a plot of the data with one fitted line per Bechdel group.

Show code

# Your code here
# Hint: You may need to clean data (remove NAs, log-transform if appropriate)

Part B: Interpretation (10 points)

In 3-4 sentences, interpret:

The coefficient for budget, as a description of these movies
The coefficient for the interaction term: how different are the two fitted lines?
The practical significance of your findings: is the difference between groups large enough to matter?

Your interpretation here:

Part C: Diagnostic Plots (10 points)

Create 2 diagnostic plots and briefly comment on whether model assumptions are reasonably met. For description, focus on whether the fitted lines are an honest summary of the data (for example, curvature, or a few huge blockbusters driving the fit).

Show code

# Your diagnostic plots here

Comment on assumptions (2-3 sentences):

Question 2: Logistic Regression (30 points)

Research Question (descriptive): Among these movies, which characteristics are associated with passing the Bechdel test? In particular, did the share of movies that pass change between 1970 and 2013, once we account for budget and IMDB rating?

You are describing which kinds of movies in this dataset tend to pass. You are not building a tool to predict whether a new movie will pass, and not claiming that a bigger budget or a better rating causes a movie to pass (or the other way around).

Part A: Model Fitting (10 points)

Fit a logistic regression model relating Bechdel test pass/fail to budget, year, and IMDB rating.

Show code

# Your code here
# Note: Create a binary outcome (0/1) from the 'binary' variable

Part B: Coefficient Interpretation (10 points)

Present a table of odds ratios with 95% confidence intervals. Interpret the odds ratio for year in context. Make sure the units of each odds ratio make sense to a reader (for example, per million dollars of budget, or per decade instead of per year).

Show code

# Your table here (consider using tidy() and exp() for odds ratios)

Interpretation (4-5 sentences):

Part C: Fitted Probabilities and Visualization (10 points)

Create a visualization showing the fitted probability of passing the Bechdel test over time (holding other variables at their means). Include confidence bands if possible.

Show code

# Your visualization here

Describe the trend (2-3 sentences):

Question 3: Comprehensive Analysis (25 points)

Research Question (descriptive): Among the movies in this dataset rated G, PG, PG-13 or R, does the relationship between budget and revenue look different across MPAA ratings?

Most movies are PG-13 or R, and there are only 36 G-rated movies, so some patterns will be much less certain than others: say so where it matters. Drop movies with other or missing ratings, and say how many you dropped.

Conduct an appropriate descriptive analysis (your choice of method, for example a regression with an interaction, or one fitted line per rating) and present your findings professionally.

Your Analysis

Show code

# Your code here

Findings

Write a brief results section (150-200 words) as if for a technical report. Include:

Description of your analytical approach
Key statistical findings
At least one figure or table
How stable your main finding is (PCS), for example to the G-rated movies or to the scale you chose
Interpretation in context of the research question

Question 4: Same Data, Different Goals (15 points)

Choose one of Questions 1-3. Suppose the goal were not description:

Inference. You want to make claims about a larger population of movies. What population could that be, and is this dataset a good sample of it? What would you change about how you choose the model, which assumptions you check, and what you report?
Prediction. You want to predict the outcome for a new movie. When would the prediction be made (for example, before release)? Which variables would actually be available at that time? How would you choose the model, measure how well it predicts, and what would you report?

Your answer (200-300 words, covering both a and b):

Submission Checklist

All code runs without errors
Code is hidden in the HTML (code-fold: true)
All interpretations are in your own words and contextual
Figures have proper labels and captions
Tables are well-formatted
Statistical results include relevant values (effect sizes, and p-values or confidence intervals where requested)
Conclusions describe these movies, with no causal claims or claims about all movies
Each model reports how many movies it uses
No AI tools were used (per the syllabus AI Policy)

References

TidyTuesday: Bechdel Test (2021-03-09). Data from FiveThirtyEight and The Bechdel Test website.
https://github.com/rfordatascience/tidytuesday/blob/master/data/2021/2021-03-09/readme.md