Business Context

HomeValue, a residential pricing platform serving 200K monthly property searches, wants a transparent baseline model for estimating sale prices from listing attributes. The pricing team needs a model trained from scratch with gradient descent so they can validate optimization behavior before moving to more complex methods.

Dataset

You are given a historical housing dataset built from MLS listings and closed sales.

• Size: 52K home sales, 18 raw features
• Target: Continuous — final sale price in USD
• Missing data: 6% missing in hoa_fee, 4% in condition_rating, 2% in school_score
• Data quality: Sale prices are right-skewed with a small number of luxury outliers above $3M

Success Criteria

A good solution should achieve RMSE below $42K and MAE below $28K on a held-out test set, while showing stable convergence of the training loss. The team also expects a clear explanation of learning rate choice, regularization, and stopping criteria.

Constraints

• Use gradient descent to train the core model rather than a closed-form solver.
• The solution must be interpretable enough to explain feature effects to pricing analysts.
• Training should complete in a few minutes on a laptop.
• Avoid data leakage from future market aggregates.

Deliverables

1. Build a regression pipeline that preprocesses mixed feature types and trains a linear model with gradient descent.
2. Explain the loss function, gradients, and how you monitor convergence.
3. Compare batch vs mini-batch gradient descent and justify your choice.
4. Evaluate on train/validation/test splits with RMSE, MAE, and R².
5. Recommend hyperparameters and production retraining cadence.