Update pages/Logistic Regression.py

pages/Logistic Regression.py

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+import streamlit as st
+
+st.set_page_config(page_title="Logistic Regression Explained", page_icon="🔍", layout="wide")
+
+# Header
+st.title("🔍 Logistic Regression (Classification)")
+
+st.markdown("""
+Logistic Regression is a **classification algorithm** used to predict the probability of a binary outcome.  
+Despite its name, it’s used for **classification**, not regression!
+""")
+
+# SECTION 1 — Concept
+with st.container():
+    st.header("🧠 Core Idea")
+    st.markdown("""
+    Logistic Regression predicts the **probability** of an event happening.  
+    It applies the **Sigmoid (Logistic)** function to a linear equation.
+    
+    **General Formula:**
+    """)
+    st.latex(r"\hat{y} = \sigma(z) = \frac{1}{1 + e^{-z}}")
+    st.latex(r"z = w_0 + w_1x_1 + w_2x_2 + ... + w_nx_n")
+    st.markdown("""
+    - \\( \hat{y} \\): predicted probability  
+    - \\( z \\): linear combination of inputs  
+    - \\( \sigma(z) \\): Sigmoid function that squashes output between 0 and 1
+    """)
+
+# SECTION 2 — How it Works
+with st.container():
+    st.header("⚙️ How Logistic Regression Works")
+    col1, col2 = st.columns(2)
+
+    with col1:
+        st.markdown("### 🧮 Step-by-step:")
+        st.markdown("""
+        1. Compute linear equation \\( z \\)  
+        2. Apply sigmoid: \\( \hat{y} = \frac{1}{1 + e^{-z}} \\)  
+        3. Threshold output:
+            - \\( \hat{y} > 0.5 \\) → Class 1  
+            - \\( \hat{y} ≤ 0.5 \\) → Class 0
+        """)
+    with col2:
+        st.image("https://upload.wikimedia.org/wikipedia/commons/8/88/Logistic-curve.svg",
+                 caption="Sigmoid Curve — S-Shaped", use_column_width=True)
+
+# SECTION 3 — Use Cases
+with st.container():
+    st.header("🚀 Real-World Use Cases")
+    st.markdown("""
+    - 🔐 Spam Detection  
+    - 🧬 Disease Diagnosis  
+    - 💳 Credit Card Fraud  
+    - 📉 Churn Prediction  
+    - 🔍 Search Ranking Classification  
+    """)
+
+# SECTION 4 — Loss Function
+with st.container():
+    st.header("❌ Loss Function: Binary Cross Entropy")
+    st.markdown("Logistic regression minimizes this loss function:")
+    st.latex(r"Loss = - \left[ y \cdot \log(\hat{y}) + (1 - y) \cdot \log(1 - \hat{y}) \right]")
+    st.markdown("""
+    - Encourages the model to assign high probabilities to the correct class.
+    - Used to update weights via **gradient descent**.
+    """)
+
+# SECTION 5 — Evaluation Metrics
+st.header("📏 Evaluation Metrics")
+
+col1, col2, col3 = st.columns(3)
+
+with col1:
+    st.subheader("✔️ Accuracy")
+    st.latex(r"Accuracy = \frac{TP + TN}{TP + TN + FP + FN}")
+    st.caption("Correct predictions over all predictions")
+
+with col2:
+    st.subheader("🎯 Precision")
+    st.latex(r"Precision = \frac{TP}{TP + FP}")
+    st.caption("How many predicted positives were actually positive?")
+
+with col3:
+    st.subheader("🔍 Recall")
+    st.latex(r"Recall = \frac{TP}{TP + FN}")
+    st.caption("How many actual positives did we catch?")
+
+col4, col5 = st.columns(2)
+
+with col4:
+    st.subheader("📊 F1-Score")
+    st.latex(r"F1 = 2 \cdot \frac{Precision \cdot Recall}{Precision + Recall}")
+    st.caption("Balances precision and recall")
+
+with col5:
+    st.subheader("🧠 ROC-AUC")
+    st.markdown("""
+    - Measures performance across all thresholds  
+    - Plots TPR vs FPR  
+    - AUC = area under ROC curve
+    """)
+
+# SECTION 6 — Key Takeaways
+st.header("📌 Summary & Tips")
+st.markdown("""
+- Logistic Regression is simple, interpretable, and works well for **linearly separable data**  
+- Assumes no multicollinearity, independent features  
+- Works best when:
+    - You need quick, interpretable results  
+    - The relationship between features and class is linear in log-odds  
+- Use regularization (`L1`, `L2`) to avoid overfitting  
+""")