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Compare RMSE and MAE

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Problem

Context

HomeValuePro uses a gradient boosting regression model to predict apartment sale prices for agents in Chicago. The model is used to set listing guidance, and leadership is debating whether to optimize for RMSE or MAE after recent complaints about a small number of very bad predictions.

Current Performance

MetricValidation SetNotes
MAE$18,400Average absolute error across all listings
RMSE$34,900Larger errors receive higher penalty
Median Absolute Error$11,200Typical listing error is lower than MAE
Mean Prediction Bias+$2,100Slight average overprediction
P90 Absolute Error$52,00010% of listings miss by more than this
Listings evaluated12,000Out-of-time validation sample

The Problem

Most predictions are reasonably close, but a small subset of luxury and newly renovated properties have very large misses. Product managers want to know whether MAE or RMSE better reflects model quality for this use case, and what the gap between the two metrics implies about the error distribution.

Requirements

  1. Explain the difference between RMSE and MAE in plain language.
  2. Interpret why RMSE ($34,900) is much higher than MAE ($18,400).
  3. Identify what this metric pattern suggests about outliers and model behavior.
  4. Recommend which metric should be prioritized for agent-facing price guidance and why.
  5. Propose concrete steps to reduce the largest errors without hurting typical-case performance.

Constraints

  • Large pricing mistakes above $75,000 create agent distrust and lost listings.
  • Small errors under $15,000 are usually acceptable in this market.
  • Retraining can happen monthly, but feature collection for new data sources is limited.