Question 9

Explanation

Correct Answer:
The data scientist failed to exponentiate the predictions in the second model prior to computing the RMSE.

Explanation:

When training a model on log-transformed labels (e.g., log(price)), the model's predictions will also be in log space. To compare these predictions to the original scale (e.g., actual price), you must reverse the transformation (exponentiate the predictions) before calculating RMSE.

Why This Matters:

1. Model 1: Predicts price directly → RMSE is calculated on the same scale.

2. Model 2: Predicts log(price) → Predictions must be exponentiated (exp(pred)) to match the price scale.

   • If not exponentiated: RMSE compares log(pred) to price, which is invalid (apples-to-oranges).

Example:

import numpy as np
from sklearn.metrics import mean_squared_error
 
# Actual prices
actual_prices = np.array([100, 200, 300])
 
# Model 1: Predicts price directly
pred_prices = np.array([110, 190, 310])
rmse1 = np.sqrt(mean_squared_error(actual_prices, pred_prices))  # Valid
 
# Model 2: Predicts log(price)
pred_log_prices = np.array([4.7, 5.2, 5.7])
 
# Incorrect RMSE (log(pred) vs. actual price)
rmse_incorrect = np.sqrt(mean_squared_error(actual_prices, pred_log_prices))  # Wrong!
 
# Correct RMSE (exp(pred) vs. actual price)
rmse_correct = np.sqrt(mean_squared_error(actual_prices, np.exp(pred_log_prices)))  # Valid

Why Other Options Are Incorrect:

1. "The second model is much more accurate":

   • Invalid because the RMSE comparison is flawed (log vs. linear scale).

2. "Failed to take the log of predictions in the first model":

   • The first model predicts price directly; no log transformation is needed.

3. "RMSE is invalid for regression":

   • RMSE is a standard metric for regression, but scale consistency is critical.

4. "The first model is more accurate":

   • The comparison is invalid unless predictions are on the same scale.

Key Takeaway:

For models trained on log-transformed labels:

1. Exponentiate predictions (exp(pred)) before calculating RMSE.

2. Compare on the original scale (e.g., price).

Impact of Skipping Exponentiation:

• RMSE will appear artificially high because log(pred) values are much smaller than price.