1. Regression and Inference
Interpret linear projections, control choices and uncertainty without manufacturing causality
1. Regression and Inference
OLS is both a descriptive projection and a component inside many research designs. Its causal meaning comes from assignment and assumptions, not from the word “regression.”
Learning outcomes
After this module, you should be able to:
- interpret OLS as a population linear projection;
- derive a slope from covariance and variance;
- use Frisch–Waugh–Lovell residualisation to explain controls;
- diagnose omitted-variable, bad-control and extrapolation risks;
- choose heteroskedasticity-robust, clustered or randomisation-based uncertainty from the design;
- report magnitude, interval and target population instead of significance alone.
Chapter route
- OLS as a Projection — what least squares estimates before causal language.
- FWL, Selection and Controls — which variation remains after adjustment.
- Inference and Clustering — what is allowed to vary and at which level.
Prepare, work, follow up
- Prepare (60 min): calculate one slope from five observations and mark each variable’s observation time.
- Workshop (120 min): reproduce naïve and adjusted Pathways estimates; construct two rival causal diagrams; defend an inference level.
- Follow up (60 min): submit a three-column table: coefficient interpretation, causal requirement and failure consequence.
Postgraduate extension: state the projection orthogonality conditions, discuss misspecification-robust inference and separate sampling-based from design-based uncertainty.