You are given a historical dataset of residential real-estate transactions — sale records with property attributes, location information, and sale dates spanning several years, including a period containing a major market shock (e.g., the COVID-19 pandemic). Build a model that predicts housing prices. This is a discussion-driven modeling case. Walk the interviewer through the end-to-end process, and expect deep, sustained follow-up questions on every design choice: how you define the outcome and the features, which model you pick and why, how you evaluate it, how you handle data-quality problems, and how you keep the model working as the market changes. ### Constraints & Assumptions - The dataset covers multiple years of transactions; some fields contain missing values. - Records include property attributes (e.g., size, rooms, age, property type), location, and the transaction date. No fixed feature list is provided — proposing and justifying features is part of the exercise. - The data window includes at least one market regime change (a shock such as COVID-19), so stationarity cannot be assumed. - Predictions are produced in batch; there is no strict serving-latency requirement unless you decide otherwise. - No coding is required, but you are expected to name concrete methods and, where relevant, write down formulas. ### Clarifying Questions to Ask - Who consumes the predictions, and at what granularity — a price estimate for an individual home at listing time, a valuation of an existing portfolio, or a price index over regions? - What exactly should the model predict: the price a home would fetch if sold today, or its price at some future date (a forecasting horizon)? - What is the geographic scope, and how heterogeneous are the markets within it? - Roughly how large is the dataset (number of transactions, years covered), and which fields have significant missingness? - Are there interpretability requirements — does a stakeholder need to understand why the model prices a specific home the way it does? - How will the model be refreshed — is periodic retraining allowed, and how quickly must it react to market moves? ### Part 1 Define the prediction target precisely and propose the feature set. How would you turn the raw transaction records into a supervised learning dataset? ```hint Target definition Raw sale prices are strongly right-skewed and span orders of magnitude across markets. Consider modeling a **transformed** target — e.g., $\log(\text{price})$ or price per unit area — and be ready to say what the transformation does to your error metric. ``` ```hint Leakage screening starts here For every candidate feature, ask: "would this value actually be known at prediction time?" Fields generated *after* or *because of* the sale (e.g., a post-sale appraisal) cannot be features. ``` #### What This Part Should Cover ```premium-lock What This Part Should Cover ``` ### Part 2 Choose a model family and defend it. Why might a non-linear model outperform linear regression on this data — what specifically about housing data makes it work? Then define your evaluation metrics and validation scheme. ```hint Why non-linear helps here Housing data is full of **interactions** (the value of an extra bedroom depends on the neighborhood) and **threshold/saturation effects** (the tenth bathroom adds little). Tree ensembles capture these automatically; a linear model needs hand-built crosses. ``` ```hint Validation with time-stamped data Random K-fold lets the model train on 2023 sales and "predict" 2021 sales — it peeks into the future. Think about a **temporal split** (train on the past, validate on a later window) and what that changes about your reported error. ``` #### What This Part Should Cover ```premium-lock What This Part Should Cover ``` ### Part 3 The dataset has missing values in several fields. How do you handle them? How do you perform feature selection, and how do you detect and prevent data leakage? ```hint Missingness is a signal Before imputing, diagnose *why* a value is missing (missing completely at random vs. related to observed vs. unobserved values). A binary "was missing" indicator column is often informative, especially for tree models. ``` ```hint The leakage smell test A feature that is *suspiciously* predictive deserves an audit of **when** it is generated. Classic housing examples: tax assessments or appraisal values recorded after the sale, or fields only populated once a listing closes. ``` #### What This Part Should Cover ```premium-lock What This Part Should Cover ``` ### Part 4 Housing markets move. After deployment, how do you detect data drift and variance drift? And how would your modeling approach have coped with a shock like COVID-19? ```hint Two different kinds of drift Separate a shift in the **input distribution** $P(x)$ from a change in the **relationship** $P(y \mid x)$, and also from a change in noise level (variance). Each shows up in different monitors — feature distributions, residuals, and interval coverage — and each calls for a different response. ``` ```hint Shock playbook Throwing away all pre-shock history is rarely the best answer. Consider **recency weighting** or rolling windows, explicit **regime indicator** features, faster retraining cadence, and widening the communicated uncertainty until the new regime stabilizes. ``` #### What This Part Should Cover ```premium-lock What This Part Should Cover ``` ### What a Strong Answer Covers ```premium-lock What a Strong Answer Covers ``` ### Follow-up Questions - Your non-linear model beats the linear baseline by a small margin. How do you decide whether the extra complexity is worth carrying in production? (Part 2) - The model systematically underprices homes in one region. Walk through your debugging process step by step. (Parts 1 and 3) - The business wants calibrated prediction intervals, not just point estimates. How do you produce and validate them? - When would you argue for separate per-region models instead of one national model, and what are the costs of that choice? (Parts 2 and 4)