1. Regression Model Metrics

Mean Squared Error (MSE)

• it is the squared of the predicted and actual values.
• Penalizes large error more strongly

Root Mean Squared Error (RMSE)

• Square root of MSE, brings error back to original value
• Easier to interpret (e.g, dollars, temperature)

Mean Absolute Error (MAE)

• Average of Absolute difference
• Less sensative to outlier than MSE

R2 Score

• Proportion of variance explained by the model
• Higher R2 = Better fit

2. Classification Model Metrics

Accuracy

• Percentage of correct predictions
• Works well if classes are balanced

Precision

• Of all predicted positive, how many are corrected?
• Important when false positives are costly (e.g, spam filter)

Recall

• Of all actual positives, How many did we catch?
• Important when false negative are costly (e.g, disease detection)

F1-Score

• Harmonic mean of precision and recall
• Balances both Metrics

Confusion Matrix

• table showing true positive, false positive, true negative, false negatives.
• Gives full picture of classification performance.

Example

Imagine a predicting whether an email is spam:

• Accuracy = 95% (most predictions correct).
• Precision = 90% (few false alarms).
• Recall = 85% (Some spam missed).
• F1 = 87% (Balanced measure).

Advanced Regression Topics

Multiple Regression

• Extend Simple regression to include multiple imput features (e.g, house size, number of rooms, location)
• Learn how coefficients represent the impact of each features

Polynomial Regression

• When data shows non-linear trends, fit curvs instead of straight lines.
• Example: predicting growth rates that accelerate over time.

Regularization

• Techniques like Ridge, Lasso, ElasticNet prevent overfitting by penalizing large coefficients.
• Ridge shrinks coefficients, lasso can eliminate irrelevant features.

Residual Analysis

• Diagnose model errors by analyzing residual plots.
• Random Scatter = good fit; patterns = model misspecification.

these are Matter Because of the following

Multiple Regression -> Handles Real World complexity. Polynomial Regression -> Captures Nonlinear Relationships. Regularization -> ensures model generalize wells Residual Analysis -> validates assumptions and detects problems