Week 8 Exercises - Does Spending More Make More?

Two predictors, one budget, and a 30-year-old confound

Overview

About 45 minutes · Pairs or small groups · 🧰 R (tidyverse, rio, here, broom) or JAMOVI

Every step is given both ways.

Part A: Follow along (~15 min): does a bigger budget buy a bigger box office?
Part B: On your own (~20 min): add year, watch the budget slope move, and explain why.
Part C: Together (~10 min): the question the data was collected to answer.

By the end you should be able to:

Fit and interpret a model with two predictors
Attach “holding ___ constant” to a coefficient and mean it
Say why a coefficient changed when a second predictor entered
Compute ΔR² and test it with a nested F
Report a null result for a predictor that a lot of people care about

Set up (5 min)

Download the data into the data folder of your PSYC 640 R Project.
- Film data (.csv)
New Quarto document, Week 8 - Multiple Regression, saved as week8_inclass.qmd.

library(tidyverse)
library(rio)
library(here)
library(broom)

films_raw <- import(here("data", "bechdel.csv"))

glimpse(films_raw)

This file is dirty on purpose

The raw dollar columns are in dollars, so every coefficient would come out in dollars and the output becomes unreadable. We will work in millions.

films <- films_raw %>%
  mutate(gross_m  = intgross_2013 / 1e6,     # international gross, $M (2013 dollars)
         budget_m = budget_2013   / 1e6,     # budget, $M (2013 dollars)
         bechdel  = factor(binary, levels = c("fail", "pass"))) %>%
  drop_na(gross_m, budget_m, year)

nrow(films)

Check yourself

1,763 films survive, spanning 1970–2013. Mean budget ≈ $55.8M, mean gross ≈ $197.9M (SD ≈ 284).

If you got 1,774, your as.numeric() step did not run and your gross variable is still text.

🖱️ In JAMOVI instead

☰ Menu → Open → Browse → bechdel.csv
JAMOVI will import intgross_2013 as Nominal (text) because of the #N/A values. Fix it in two steps:
- Double-click the intgross_2013 column header → change Measure type to Continuous. The #N/A cells become missing.
- Data → Compute, new variable gross_m, formula: intgross_2013 / 1000000
Data → Compute, new variable budget_m, formula: budget_2013 / 1000000
Confirm under Exploration → Descriptives that gross_m has N = 1763 and budget_m has a mean near 55.8.

All dollar figures below are in millions of 2013 dollars. Say so in your write-up; a coefficient without units is not a finding.

Part A — Follow along (15 min)

A1. Look before you model

films %>%
  select(year, budget_m, gross_m) %>%
  psych::describe(fast = TRUE)

films %>%
  ggplot(aes(x = budget_m, y = gross_m)) +
  geom_point(alpha = .3) +
  geom_smooth(method = "lm", se = FALSE, color = "#B3261E") +
  labs(x = "Budget ($M)", y = "International gross ($M)",
       title = "Bigger budgets, bigger returns?") +
  theme_bw()

🖱️ In JAMOVI

Exploration → Descriptives: year, budget_m, gross_m into Variables; check Mean, SD, Minimum, Maximum
Exploration → scatr → Scatterplot: budget_m on X, gross_m on Y, Regression Line = Linear

Q1. Describe the cloud. Where do most films sit, and what does the handful of points in the upper right do to a regression line?

A2. One predictor

mod_budget <- lm(gross_m ~ budget_m, data = films)

summary(mod_budget)
#glance(mod_budget) %>% select(r.squared, adj.r.squared, sigma)

🖱️ In JAMOVI

Regression → Linear Regression: gross_m → Dependent Variable, budget_m → Covariates. Under Model Coefficients check Estimate and Standard error; under Model Fit check R², Adjusted R² and Overall model test (F test).

Check yourself

b₀ = 27.47, b₁ = 3.054, R² = .349, RSE = 229.2, F(1, 1761) = 945.85

Q2. Interpret budget_m in a sentence a studio executive would understand. Include the units.

Q3. The intercept is 27.47. What film does that describe, and is it a film that exists?

Q4. R² = .349 and RSE = 229. Put the RSE in plain language: when this model guesses a film’s gross, how far off is it typically? Compare that to the SD of gross_m (284).

Part B — On your own (20 min)

The data span 1970 to 2013. That is four decades of changing audiences, changing numbers of theaters, and changing release strategies — all inside one regression that pretends they are the same.

B1. Does year matter on its own?

mod_year <- lm(gross_m ~ year, data = films)
summary(mod_year)
#glance(mod_year) %>% select(r.squared, adj.r.squared)

Q5. Year alone: R² = .019, b = −4.32. Write the interpretation. Does the sign surprise you? (Remember every dollar here is already inflation-adjusted to 2013.)

B2. Now both

mod_both <- lm(gross_m ~ budget_m + year, data = films)
summary(mod_both)
#glance(mod_both) %>% select(r.squared, adj.r.squared, sigma)

🖱️ In JAMOVI

Same Linear Regression panel — drag year into Covariates alongside budget_m. JAMOVI updates the coefficient table immediately.

Check yourself

	b	p
intercept	11654.52	< .001
`budget_m`	3.127	< .001
`year`	−5.808	< .001

R² = .3829, adj. R² = .3822, RSE = 223.3

Q6. Interpret both coefficients, each with its holding constant clause.

Q7. The budget slope went up: 3.054 → 3.127. Most people expect a coefficient to shrink when you add a control. Use these three correlations to explain why this one grew:

Note

Try to use the sjPlot library to make it look nice!

films %>% select(year, budget_m, gross_m) %>% cor() %>% round(3)

🖱️ In JAMOVI

Regression → Correlation Matrix: all three variables into the box.

Hint

year is positively related to budget (r = .08) and negatively related to gross (r = −.14). So part of what made the raw budget slope look smaller was that expensive films are disproportionately recent, and recent films gross less. Hold year still and the budget effect comes through a little more cleanly. This is the same machinery as Lab 8’s suppression, in a gentler form.

B3. Did year earn its place?

anova(mod_budget, mod_both)

🖱️ In JAMOVI

Use Model Builder: put budget_m in Block 1, click + Add New Block and put year in Block 2. Then open Model Comparisons — JAMOVI reports ΔR² and the F test for the added block directly.

Q8. Report ΔR² and the nested F in APA format. Then answer in one sentence: did adding year improve the model enough to keep it?

Q9. Adjusted R² also rose (.3491 → .3822). Why do we check adjusted R² here rather than just R²?

Q10. Use the model to predict the international gross of a $50M film released in 2013, and of a $50M film released in 1980.

predict(mod_both, newdata = tibble(budget_m = 50, year = c(2013, 1980)))

Which prediction would you trust more, and why?

Part C — Together (10 min)

C1. The reason this dataset exists

The binary column records whether a film passes the Bechdel test: does it have at least two named women who talk to each other about something other than a man? A common industry claim is that films centered on women are a worse financial bet.

Start with the raw comparison:

films %>%
  group_by(bechdel) %>%
  summarise(n = n(),
            mean_gross  = mean(gross_m),
            mean_budget = mean(budget_m))

What you get

	n	mean gross	mean budget
fail	972	223.3	63.5
pass	791	166.6	46.4

Q11. Taken alone, films that pass gross about $57M less. Before you conclude anything — what else is different about those two groups in that table?

C2. Ask it properly

mod_bechdel <- lm(gross_m ~ budget_m + year + bechdel, data = films)
summary(mod_bechdel)

anova(mod_both, mod_bechdel)

🖱️ In JAMOVI

Drag bechdel into Factors (not Covariates — it is categorical). Under Reference Levels, confirm the reference is fail. Add it as Block 3 in Model Builder to get its ΔR².

What you get

bechdel (pass vs. fail): b = +5.96, SE = 10.88, t = 0.55, p = .584

ΔR² = .0001, F(1, 1759) = 0.30, p = .584

❓Questions for Part C

The raw difference was −$57M. Controlling for budget and year it is +$6M, non-significant. Explain to a producer what happened — in words, not in regression vocabulary.
Write the APA sentence reporting this null result. Then write the sentence you would put in the discussion section.
Someone reads your output and says “so the Bechdel test doesn’t matter.” Give two different things your model cannot tell them.
Films that pass have budgets averaging $46M vs $63M for films that fail. Your model treats that as a nuisance to control away. What if it is the actual finding?

The point of Part C

“Control for the obvious confound” is not a technicality — it is sometimes the whole result. The raw gap was real and the adjusted gap is roughly zero, and which of those two numbers answers the question depends entirely on what question you asked. The model cannot tell you that part.

Exit ticket ✅

In your own words: what does “holding X constant” let you compare?
A colleague says “my R² went up, so the new predictor helped.” What do you ask them for?
One thing that is still muddy → journal.