Regression analysis applications: (1) Prediction: Estimate y for new x values; (2) Relationship quantification: Measure strength and direction; (3) Hypothesis testing: Determine if relationship significant; (4) Forecasting: Project future values; (5) Causal inference: Investigate dependencies. Confidence intervals: ŷ ± t×SE (standard error). Example: Predicting house price from square footage. Model: Price = 50000 + 150×sqft. For 2000 sqft: Predicted price = 50000 + 300000 = 350000. 95% CI might be [330000, 370000]. Applications: Finance (stock returns), economics (GDP), business (sales forecasting). Exam tip: Understand prediction vs causation. Report confidence intervals. Check residuals.