Statistics Quest

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:

  1. Which property features are associated with price, and by how much — in terms a credit officer understands?
  2. Why do some colleagues say “bedrooms add SAR 290,000 each” while others find bedrooms add almost nothing?
  3. 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

SaleSale dateDistrictFloor area (m²)BedroomsBathroomsBuilding age (years)Distance to centre (km)GarageSale price (SAR)
H00012023-06-07Desert Edge35353621.8true1005000
H00022023-06-13Desert Edge219432228.2false430000
H00032023-06-07Lakeside29443288.8true1473000
H00042023-05-03Desert Edge16532223.3true543000
H00052023-08-11Palm Grove1523299.1false792000
H00062023-01-21Hillcrest259431513.6false1310000

Included with a Formula Quest membership

This case has 4 stages and 9 graded tasks, ending with a written report.

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