You are asked to build a model of monthly rents for 5,000 Mumbai flats from carpet area, floor, distance to the nearest station and building age. Choose the target, the features and the validation scheme, and interpret a coefficient of 0.9 on log area.

Model log rent, use log area, floor, log distance, age and locality, validate by holding out whole buildings and the latest months, and read 0.9 as an elasticity: a 10% larger flat rents for about 9% more. Logs turn a fanning spread into even percentage errors. Random splits would leak building quality between training and test and flatter the error. Convert predictions back with a small correction, since exponentiating predicted log rent understates the average.

Rents in Mumbai run from about Rs 15,000 to several lakh, and the errors grow with the rent: a model that is Rs 5,000 off on a Rs 25,000 flat is badly wrong, while the same miss on a Rs 2 lakh flat is excellent. Taking logs makes errors roughly proportional, so the model is judged on percentage misses, and it turns the multiplicative way prices work, location times size times condition, into a sum a linear model can fit. The left panel below shows the raw spread fanning out as flats get bigger; the right shows the same points with an even spread around a straight line once both axes are logged.

In a model with logs on both sides, the coefficient is an elasticityThe percentage change in one quantity that goes with a 1% change in another.. A 0.9 means a 1% larger flat rents for about 0.9% more, so 10% more area gives 1.1 to the power 0.9 = 1.0896, about 9.0% more rent. A 500 square foot flat at Rs 40,000 becomes about Rs 43,583 at 550 square feet, other things equal; doubling the area raises rent by 87%, not 100%. Because 0.9 is below 1, rent per square foot falls slightly with size, by about 0.9% for each 10% more area, which matches how larger flats are actually let.

Locality is the feature that matters most and the one candidates forget. Rent per square foot can differ several times between two Mumbai localities, so without locality effects the area coefficient soaks up location, because bigger flats cluster in some areas. Use distance to the station in logs, since the first kilometre matters far more than the fifth. Floor is not straight-line either: ground floors and very high floors in old buildings without lifts often rent lower, so use bands or a curve, and add a lift flag if the data has it. Age enters in bands, because a new building and a 40-year-old one differ in kind as well as degree.

Ask what the model will face: new flats next quarter, many in buildings it has never seen. A random split puts flats from the same building in both training and test sets, so the model is graded partly on memorised building quality and its error looks smaller than it will be. Hold out whole buildings in cross-validation, and keep the most recent quarter as a final test so time trends in rent are not leaked backward. Report median absolute percentage error, which a client understands. Finally, when converting back to rupees, exponentiating predicted log rent gives a median, not a mean; with residual spread of about 0.25 in logs, multiply by about 1.032 if you need the average rent.