Regression Applications
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# Regression Applications ## Forecasting Use time as a predictor: $y_t = \beta_0 + \beta_1 t + \varepsilon_t$ **Example:** Predict next quarter's sales based on historical trend. ## Causal Inference Regression can estimate causal effects **if** all confounders are controlled for.
Regression Applications
Forecasting
Use time as a predictor:
Example: Predict next quarter's sales based on historical trend.
Causal Inference
Regression can estimate causal effects if all confounders are controlled for.
Example: Does education affect earnings? Regress earnings on years of education, controlling for ability, experience, and demographics.
Warning: "Correlation does not imply causation." Omitted variable bias is a serious concern.
Prediction vs. Inference
| Goal | Focus | Key Metric |
|---|---|---|
| Inference | Understand relationships | Coefficient estimates, p-values |
| Prediction | Forecast new outcomes | R-squared, prediction error, cross-validation |