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+---
+id: bc1e54196f
+question: Why does my logistic regression validation AUC drop vs the single feature
+  AUC, and why does `C=0.001` beat `C=1`?
+sort_order: 37
+---
+
+Your model isn’t broken—this behavior usually comes from feature scaling interacting with L2 regularization.
+
+In the homework setup, one numeric column (e.g. `annual_income`) can have a much larger scale (tens of thousands) than the other features (often 0–10 or one-hot 0/1). Logistic regression with regularization (scikit-learn’s default L2 penalty) is not scale-invariant, so the optimizer will let the large-magnitude feature dominate when `C` is larger.
+
+As a result:
+- With larger `C` (weaker regularization, e.g. `C=1`), the model can over-rely on the unscaled `annual_income` column, making the score ranking on validation worse than ranking by `lead_score` alone.
+- With smaller `C` (stronger regularization, e.g. `C=0.001`), the weights shrink, limiting how much the unscaled income feature can distort the fit—so validation AUC improves.
+
+How to fix (recommended for your own modeling):
+1. Scale numeric columns using `fit` on the training data only.
+2. Apply the same scaler to validation/test.
+3. Then proceed with `DictVectorizer` (fit on train, transform val) and train logistic regression.
+
+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
+```
+
+Important for the homework answers:
+- If you’re submitting the specific values the questions ask for, use the required preprocessing (the unscaled setup). In that case, lower validation AUC (e.g. ~0.732) and `C=0.001` beating `C=1` are expected.
+
+Takeaways:
+- Always compare against the best single-feature baseline.
+- For regularized linear models, scale numeric features.
+- Hyperparameters like `C` may appear to “flip” depending on whether features are on comparable scales.
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