When learning regression models (Linear Regression, Logistic Regression, etc.), students often face various challenges. Here are some common problems and their solutions:
1. Multicollinearity 
Problem:
- Independent variables (features) are highly correlated with each other, leading to unstable coefficient estimates.
- Causes inflated standard errors and unreliable predictions.
Solution:
1. Use Variance Inflation Factor (VIF) to detect multicollinearity.
2. Remove one of the correlated variables or use Principal Component Analysis (PCA).
3. Use Ridge Regression (L2 Regularization) to reduce coefficient variance.
2. Overfitting & Underfitting 
Problem:
- Overfitting: The model captures noise instead of the actual pattern.
- Underfitting: The model is too simple and fails to capture relationships in data.
Solution:
1. Use Regularization (L1, L2) to prevent overfitting.
2. Ensure enough training data to generalize well.
3. Feature selection to remove unnecessary features.
4. Try Polynomial Regression if the relationship is non-linear.
3. Non-Linearity in Data 
Problem:
- Linear Regression assumes a linear relationship between independent and dependent variables.
- If the actual relationship is non-linear, the model will perform poorly.
Solution:
1. Use Polynomial Regression to model non-linearity.
2. Try Non-linear models like Decision Trees, Random Forest, or Neural Networks.
3. Apply log transformation or other mathematical transformations.
4. Heteroscedasticity (Unequal Variance) 
Problem:
- The variance of residuals is not constant across all levels of independent variables.
- It leads to unreliable coefficient estimates.
Solution:
1. Use log transformation to stabilize variance.
2. Check for heteroscedasticity using Residual Plot.
3. Apply Weighted Least Squares Regression (WLS).
5. Outliers & Influential Points 
Problem:
- Outliers distort regression coefficients and predictions.
Solution:
1. Use Boxplots or IQR (Interquartile Range) to detect outliers.
2. Use Robust Regression or Remove Outliers if they are errors.
3. Try Winsorization (capping extreme values) instead of removing outliers.
6. Data Leakage 
Problem:
- Using information in training that won’t be available in real-world predictions.
- Leads to artificially high accuracy and poor generalization.
Solution:
1. Always split data before feature engineering.
2. Remove future-dependent variables (e.g., using revenue to predict sales).
3. Use proper cross-validation techniques.
7. Improper Train-Test Split 
Problem:
- Not splitting data properly can cause biased models.
- If test data leaks into training, the model performs well artificially.
Solution:
1. Use train-test split (80%-20%) properly.
2. For time-series data, use Time Series Split instead of random splitting.
8. Feature Scaling Issues 
Problem:
- Regression models with distance-based features (e.g., Polynomial Regression, Gradient Descent) perform poorly if features are on different scales.
Solution:
1. Use Standardization (Z-score scaling) for normally distributed data.
2. Use Min-Max Scaling (Normalization) if data has outliers.
9. Missing Values 
Problem:
- Regression models don’t handle missing values well, leading to errors.
Solution:
1. Use Mean/Median/Mode Imputation if missing values are few.
2. Try KNN or MICE Imputation for better predictions.
3. If too many values are missing, consider dropping the feature.
10. Assumption Violations (Linear Regression) 
Problem:
- Linear Regression assumes:
- Linearity
- No Multicollinearity
- Homoscedasticity (Equal variance)
- Normally distributed residuals
- Violating these can lead to incorrect predictions.
Solution:
1. Use diagnostic plots (residual plots, Q-Q plots) to check assumptions.
2. Apply transformations (log, square root) to fix violations.
3. Use Generalized Linear Models (GLMs) if assumptions don’t hold.
Key Takeaways
Check for multicollinearity using VIF. Handle outliers & missing values properly. Apply feature scaling when needed. Test for heteroscedasticity and apply transformations. Split data properly to avoid leakage.
