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unit 2/04_Model_Evaluation.md

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+# Model Evaluation Metrics
+
+How do we know if our classification model is good? We use several metrics.
+
+## Confusion Matrix
+A table that compares **Predicted** values with **Actual** values.
+
+| | Predicted Negative | Predicted Positive |
+|---|---|---|
+| **Actual Negative** | True Negative (TN) | False Positive (FP) |
+| **Actual Positive** | False Negative (FN) | True Positive (TP) |
+
+- **TP**: Correctly predicted positive.
+- **TN**: Correctly predicted negative.
+- **FP**: Incorrectly predicted positive (Type I Error).
+- **FN**: Incorrectly predicted negative (Type II Error).
+
+## Key Metrics
+
+### 1. Accuracy
+- Fraction of **all** correct predictions.
+- **Formula**: `(TP + TN) / Total`
+- **Problem**: Not reliable if data is imbalanced (Accuracy Paradox).
+
+### 2. Precision
+- Out of all predicted positives, how many were actually positive?
+- **Formula**: `TP / (TP + FP)`
+- Higher is better.
+
+### 3. Recall (Sensitivity / TPR)
+- Out of all **actual** positives, how many did we find?
+- **Formula**: `TP / (TP + FN)`
+- Higher is better.
+
+### 4. Specificity
+- Out of all **actual** negatives, how many did we correctly identify?
+- **Formula**: `TN / (TN + FP)`
+
+### 5. F1 Score
+- The harmonic mean of Precision and Recall.
+- Good for balancing precision and recall, especially with uneven classes.
+- **Formula**: `2 * (Precision * Recall) / (Precision + Recall)`
+
+## ROC and AUC
+
+### ROC Curve (Receiver Operating Characteristic)
+- A plot of **TPR (Recall)** vs **FPR (False Positive Rate)**.
+- Shows how the model performs at different thresholds.
+
+### AUC (Area Under the Curve)
+- Measures the entire area underneath the ROC curve.
+- **Range**: 0 to 1.
+- **Interpretation**: Higher AUC means the model is better at distinguishing between classes.