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+---
+id: f5edae392a
+question: 'Homework Q4: Logistic regression validation AUC is worse than the single
+  feature `lead_score`—is the model broken?'
+sort_order: 7
+---
+
+No—your model isn’t broken. In this homework, the drop comes from feature scaling, not from the evaluation code.
+
+`annual_income` is on the order of ~50,000, while most other features are between 0 and 10 (and one-hot columns are 0/1). Logistic regression with L2 regularization (e.g., sklearn’s default) is not scale-invariant, so the large unscaled `annual_income` column can dominate the fit when you use a larger `C`.
+
+That’s why:
+- `lead_score` alone can achieve a higher ROC AUC in Q1.
+- The full model with `C=1` can underperform because the learned weights end up being shaped mainly by the unscaled income scale.
+- With stronger regularization (smaller `C`, e.g. `C=0.001`), the weights are shrunk, which reduces the distortion from the unscaled income column—so it can look better.
+
+The fix is to scale numeric columns using only the training split, then reuse the same scaler for validation.
+
+Example:
+
+```python
+from sklearn.preprocessing import StandardScaler
+
+numerical = [
+    "number_of_courses_viewed",
+    "annual_income",
+    "interaction_count",
+    "lead_score",
+]
+
+scaler = StandardScaler().fit(df_train[numerical])
+
+df_train[numerical] = scaler.transform(df_train[numerical])
+df_val[numerical] = scaler.transform(df_val[numerical])
+
+# then continue with DictVectorizer + LogisticRegression as usual
+```
+
+After scaling, `C` should have little effect on AUC, because the feature scales are comparable. Also remember for the homework: if the instructions ask you to submit the unscaled values for the reported answers, submit those (e.g., ~0.732 for Q2 and the `C=0.001` result), even if scaling would improve performance.
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