How fast do cars lose value? Modelling depreciation from listings

AI SLAI HLAA SL Accessible Also in: Modelling, Statistics

Research question

Is the price of [a car model] better modelled as a linear or exponential function of age, what annual depreciation rate does the exponential model imply, and does mileage explain the residuals?

Adapt it: change the place, the data or the comparison until the question is yours.

Why it makes a good exploration

Depreciation is often quoted as a fixed percentage per year. Collecting real listings and testing that claim is simple to do, statistically rich and useful.

The mathematics you'll need

Linear and exponential regression
Logarithmic transformation
Interpreting the fitted rate as percentage depreciation
Residuals vs a second variable (mileage)

Course labels show where a technique sits; using maths from outside your course is fine if you explain it clearly and say it is new to you.

Where the data comes from

Record price, age and mileage from 50+ listings of one model on a used-car website.

Desmos graphing calculator — Free graphing and regression (y₁ ~ ax₁ + b) — fit models to your data and show residuals.

Cite every source in a footnote where you use it and in your bibliography. Check the licence of any dataset you download.

A possible outline

Choose one model and trim level.
Collect listings in one period.
Fit and compare models.
Examine residuals against mileage.
Reflect on listing price vs selling price.

Pitfalls that cost marks

Mixing trims, engines or conditions.
Using asking prices without comment.
Too few old cars.

Showing personal engagement

Choose a car your family owns.
Compare two brands' depreciation rates.
Predict your family car's value and check a valuation site.

See Criterion C: personal engagement for what examiners look for.

Taking it further

Fit a model with both age and mileage and compare its predictions.

See it done

Our annotated exemplar Should I lease or buy my first car? (AI SL) explores a question like this one, with an examiner's comment on every criterion.

Turn this idea into your IA

Plan this IAOpens the planner with this question, the maths and data sources filled in. Desmos workspacePlot your data, fit models and keep your graphs with your plan. AI feedback on a draftCriterion-by-criterion feedback with evidence from your own text. Coaching, not rewriting. Examiner reviewPete, a practising IA examiner, reads your draft and talks it through with you (€100).