What Regression Does

Goal: Predict a continuous outcome from one or more input variables

Example: Predict house price from size, bedrooms, and location

Reading the Output

Coefficient (slope): Change in Y when X increases by 1 unit

• Size coefficient = 150 → Each extra sqft adds $150 to price
• Negative coefficient → Inverse relationship

R-squared: Percentage of variance explained

• R² = 0.85 → Model explains 85% of variation in Y
• Higher is better, but context matters

Key Assumptions (Check These!)

1. Linear relationship - Plot X vs Y to verify
2. Independent observations - No repeated measurements
3. Homoscedasticity - Error variance is constant
4. Normal residuals - For small samples especially

Common Mistakes

❌ Extrapolating beyond your data range - Model doesn't know what happens outside training range

❌ Ignoring multicollinearity - Correlated predictors make coefficients unstable

❌ Using R² alone to judge model - Plot residuals to check assumptions

Quick Decision Tree

• Predicting continuous outcome → Linear regression
• Predicting binary outcome (yes/no) → Logistic regression
• Non-linear patterns → Try polynomial terms or other models