Update pages/Linear Regression.py

pages/Linear Regression.py

@@ -59,14 +59,40 @@ st.markdown("""
 - **No multicollinearity**: Independent variables aren't too correlated
 """)
 
-# Metrics
 st.markdown("### 📏 Evaluation Metrics")
-st.markdown("""
-- **Mean Absolute Error (MAE)**  
-- **Mean Squared Error (MSE)**  
-- **Root Mean Squared Error (RMSE)**  
-- **R² Score (Coefficient of Determination)**  
-""")
+
+with st.expander("1️⃣ Mean Absolute Error (MAE)"):
+    st.latex(r"MAE = \frac{1}{n} \sum_{i=1}^{n} \left| y_i - \hat{y}_i \right|")
+    st.markdown("""
+    - Measures the average magnitude of errors.
+    - It’s easy to understand and not sensitive to outliers.
+    - **Lower MAE = better model**.
+    """)
+
+with st.expander("2️⃣ Mean Squared Error (MSE)"):
+    st.latex(r"MSE = \frac{1}{n} \sum_{i=1}^{n} (y_i - \hat{y}_i)^2")
+    st.markdown("""
+    - Measures average of squared errors.
+    - Penalizes larger errors more than MAE.
+    - Sensitive to outliers.
+    """)
+
+with st.expander("3️⃣ Root Mean Squared Error (RMSE)"):
+    st.latex(r"RMSE = \sqrt{\frac{1}{n} \sum_{i=1}^{n} (y_i - \hat{y}_i)^2}")
+    st.markdown("""
+    - Square root of MSE.
+    - Interpreted in the same units as the output variable.
+    - Also penalizes large errors.
+    """)
+
+with st.expander("4️⃣ R² Score (Coefficient of Determination)"):
+    st.latex(r"R^2 = 1 - \frac{\sum (y_i - \hat{y}_i)^2}{\sum (y_i - \bar{y})^2}")
+    st.markdown("""
+    - Indicates how much variance in the target is explained by the model.
+    - Ranges from **0 to 1** (sometimes negative if the model is worse than the mean).
+    - **Closer to 1 = better model**.
+    """)
+
 
 # Visualization and Prediction Explanation
 st.markdown("### 📉 Visual Representation")