Applied case · Real estate and lending · about 75 minutes
What drives house prices?
Build a valuation model for 800 home sales: choose the right scale for price, untangle floor area from bedrooms, interpret log-scale coefficients as percentages and give an honest prediction interval for a single home.
The brief
A mortgage lender's collateral valuation team checks every appraisal it receives against a statistical benchmark. Appraisals far outside the benchmark range go to a senior valuer, which costs time and delays the loan. The team asks you to build that benchmark for Wadi Noor, a fictional city with five districts, from 800 villa and townhouse sales registered in 2023 (dataset housing, synthetic).
The team needs answers to three practical questions:
- Which property features are associated with price, and by how much — in terms a credit officer understands?
- Why do some colleagues say “bedrooms add SAR 290,000 each” while others find bedrooms add almost nothing?
- For a specific property, what range of prices is normal, so that an appraisal outside it is flagged?
The decision that depends on your work: where to set the flagging range. Too narrow and valuers drown in false alarms; too wide and inflated appraisals slip through, putting the lender's collateral at risk.
All sales are synthetic and generated for teaching; they describe no real city or market.
Dataset
Home sales in a fictional city
800 rows · one row = one property sale · synthetic data
| Sale | Sale date | District | Floor area (m²) | Bedrooms | Bathrooms | Building age (years) | Distance to centre (km) | Garage | Sale price (SAR) |
|---|---|---|---|---|---|---|---|---|---|
| H0001 | 2023-06-07 | Desert Edge | 353 | 5 | 3 | 6 | 21.8 | true | 1005000 |
| H0002 | 2023-06-13 | Desert Edge | 219 | 4 | 3 | 22 | 28.2 | false | 430000 |
| H0003 | 2023-06-07 | Lakeside | 294 | 4 | 3 | 28 | 8.8 | true | 1473000 |
| H0004 | 2023-05-03 | Desert Edge | 165 | 3 | 2 | 2 | 23.3 | true | 543000 |
| H0005 | 2023-08-11 | Palm Grove | 152 | 3 | 2 | 9 | 9.1 | false | 792000 |
| H0006 | 2023-01-21 | Hillcrest | 259 | 4 | 3 | 15 | 13.6 | false | 1310000 |
Included with a Formula Quest membership
This case has 4 stages and 9 graded tasks, ending with a written report.
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