Fitting and breaking models

Research Skills — Week 8 Application

Today’s plan

Today’s plan

• Brief guided example
• Group work
• Extrapolation exercise
• Discussion
• Wrap-up

Two parts

Part	Time	What
Regression	45 min	Apply lm() to your project (if relevant)
Extrapolation	25 min	A structured exercise everyone does

• [16:05–16:15] Setup: pull latest changes. Today has both project work and a shared exercise.

Questions?

Submit questions:

PollEv.com/geol

text geol to 07480 781235

• Open the Poll Everywhere Q&A activity before the session and leave it active throughout.
• Questions appear in your Poll Everywhere presenter view; upvoted questions rise to the top.
• Address during transitions or at the end of concept blocks, not mid-explanation.
• Reset (archive) the activity between sessions so questions don’t carry over from the previous week.

Brief guided example

• Today’s plan

Brief guided example

🎓💻 Quick demo

• Group work
• Extrapolation exercise
• Discussion
• Wrap-up

Regression workflow

1. Fit lm(y ~ x, data = df)
2. summary() — coefficients, R²
3. plot(model) — diagnostics
4. Interpret: slope, R², residual patterns

• [16:15–16:30] Keep it brief — but still type it, don’t paste it. Students have seen this in the content session, so this is the ideal slide to say “you have the same four steps I do; see if you can beat me to the R²” and start typing a minute later.

• Anticipated code — wind plus solar since 2010, which is exactly the series Exercise 1 on the exercise page builds:

  elec <- read.csv("data/uk_electricity.csv")
  elec$renewable_twh <- elec$wind_twh + elec$solar_twh
  recent <- elec[elec$year >= 2010, ]
  
  model <- lm(renewable_twh ~ year, data = recent)
  summary(model)
  
  plot(model)

• Numbers to narrate: slope 6.64 TWh per year, R² = 0.978, p = 4.7e-13, residual SE 4.86 on 14 df. “Renewables have added about 6.6 TWh a year since 2010, and a straight line accounts for 97.8% of the variation.”

• Then ask the Week 8 question: R² = 0.978 and the residuals still curve. plot(model) panel 1 is where that shows. A very high R² is not the same as a model that captures the process — which is the extrapolation trap the exercise page walks into next.

Group work

• Today’s plan
• Brief guided example

Group work

✏️💻 Regression on your data

• Extrapolation exercise
• Discussion
• Wrap-up

Your analysis

Groups with a regression question: fit and diagnose.

Groups with t-test/ANOVA: refine existing analyses — add effect sizes, improve figures, document assumptions.

All groups: write a Methods and Results section draft.

• [16:30–17:00] Circulate. By this point groups should have substantive analysis to show. Flag any who are falling behind.

Extrapolation exercise

• Today’s plan
• Brief guided example
• Group work

Extrapolation exercise

✏️💻 Breaking a model

• Discussion
• Wrap-up

UK renewable energy: 2010–2025

Everyone does this exercise, regardless of project topic.

The WebR page has scaffolded exercises:

1. Fit a linear model to the renewable trend. Plot it.
2. Extrapolate to 2040. What does it predict?
3. Fit an exponential model. Extrapolate to 2040.
4. Which is better? Is either plausible?
5. What is the model not capturing?

• [17:00–17:25] Both models “fit” the historical data well. Neither predicts the future correctly. The linear model underestimates; the exponential overestimates absurdly.
• Students should identify: planning constraints, grid limits, saturation effects, policy changes.

Attendance

Show the QR from https://attendance.durham.ac.uk/mytimetable, then ← back to the task.

Discussion

• Today’s plan
• Brief guided example
• Group work
• Extrapolation exercise

Discussion

💬 What did you find?

• Wrap-up

The extrapolation lesson

• Both models fit the data well in-sample
• Both produce absurd predictions out-of-sample
• In-sample quality tells you nothing about out-of-sample quality

“What is the model not capturing?”

The question that separates a good analyst from HolmesCo.

Your project

“In our project, the biggest thing our analysis might be missing is…”

• [17:25–17:40] Groups share their reflections. This builds toward the limitations section of their reports.

Wrap-up

• Today’s plan
• Brief guided example
• Group work
• Extrapolation exercise
• Discussion

Wrap-up

Any questions we missed?

Submit questions:

PollEv.com/geol

text geol to 07480 781235

• Continuation of the same Poll Everywhere Q&A activity opened at the start of the session — this is not a new poll, so don’t reset/archive it yet.
• Surface any questions that have come in since the early Questions slide, especially ones raised during today’s content.
• Once you’ve finished with this slide, archive (reset) the activity at the end of the session so questions don’t carry over.

Commit your work

Commit all analysis code and results.

Your analysis is now nearly complete.

Next two weeks: refine, write up, and have it reviewed.

• Check the Q&A — surface any top-voted questions before finishing.
• Students should be producing report-quality analysis. Check each group’s progress.