🔢 Purpose¶
This companion focuses on visual evaluation and diagnostics after fitting a linear regression model. It complements pre-modeling EDA workflows and ensures your model outputs are thoroughly analyzed before final acceptance.
🔢 1. Actual vs Predicted Plot¶
Goal: Check how well predicted values match true values.
import seaborn as sns
import matplotlib.pyplot as plt
plt.figure(figsize=(6,6))
sns.scatterplot(x=y_test, y=y_pred)
plt.plot([y_test.min(), y_test.max()], [y_test.min(), y_test.max()], 'r--') # 45-degree line
plt.xlabel('Actual Values')
plt.ylabel('Predicted Values')
plt.title('Actual vs Predicted')
plt.show()
| What to Look For |
|---|
| Points clustered around red line ✅ Good predictions |
| Systematic deviation from line ⚠️ Bias or underfitting |
📊 2. Residuals vs Predicted Plot¶
Goal: Check homoscedasticity (constant variance of errors).
residuals = y_test - y_pred
plt.figure(figsize=(6,4))
sns.scatterplot(x=y_pred, y=residuals)
plt.axhline(0, color='red', linestyle='--')
plt.xlabel('Predicted Values')
plt.ylabel('Residuals')
plt.title('Residuals vs Predicted Values')
plt.show()
| What to Look For |
|---|
| Random cloud around 0 ✅ Homoscedastic |
| Funnel shape ⚠️ Heteroskedasticity |
| Curve shape ⚠️ Misspecified model |
📁 3. Histogram of Residuals¶
Goal: Check if residuals are approximately normally distributed.
sns.histplot(residuals, kde=True)
plt.title('Histogram of Residuals')
plt.xlabel('Residual')
plt.show()
| What to Look For |
|---|
| Bell-shaped curve ✅ Normality assumption good |
| Skewed or multi-modal ⚠️ Possible issues |
📋 4. QQ Plot of Residuals¶
Goal: Further assess normality of errors.
import statsmodels.api as sm
sm.qqplot(residuals, line='45')
plt.title('QQ Plot of Residuals')
plt.show()
| What to Look For |
|---|
| Points along 45° line ✅ Good normality |
| Systematic bends ⚠️ Skewness or heavy tails |
📊 5. Key Model Metrics¶
Goal: Report numerical evaluation of model quality.
from sklearn.metrics import mean_squared_error, mean_absolute_error, r2_score
mse = mean_squared_error(y_test, y_pred)
rmse = mse ** 0.5
mae = mean_absolute_error(y_test, y_pred)
r2 = r2_score(y_test, y_pred)
print(f'RMSE: {rmse:.4f}')
print(f'MAE: {mae:.4f}')
print(f'R²: {r2:.4f}')
| Metric | Meaning |
|---|---|
| RMSE | Root mean square error (penalizes big errors) |
| MAE | Mean absolute error (straight average error) |
| R² | Variance explained by model |
📖 6. Model Complexity and Selection (Optional)¶
Goal: Compare models if fitting multiple.
print(f'AIC: {model.aic}')
print(f'BIC: {model.bic}')
| What to Look For |
|---|
| Lower AIC/BIC ✅ Better model fit given complexity |
| Big drop moving to higher-order polynomials? ⚠️ Risk of overfitting |
📈 Visual Evaluation Checklist¶
- [ ] Actual vs Predicted: Points along 45° line?
- [ ] Residuals vs Predicted: Random spread around 0?
- [ ] Histogram of Residuals: Bell-shaped?
- [ ] QQ Plot: Points fall along line?
- [ ] RMSE, MAE, R² reported?
- [ ] AIC/BIC if comparing models?
💚 Final Analyst Tip¶
Always combine visual evaluation + metric reporting to build the most credible, transparent, and defensible linear regression models!