OLS and multiple linear regression
Estimate a conditional mean in outcome units
Ordinary least squares estimates a linear conditional-mean model by minimising squared residuals. Simple regression uses one predictor; multiple regression includes several, with categorical indicators, interactions and transformations when justified. Linear refers to coefficients, so curved predictor relationships can be represented. Interpretation depends on the covariates held fixed and the study design.
Use to explain associations or predict a continuous outcome when a defensible conditional-mean model is available. Identify the estimand, plausible confounders, dependence structure and prediction population before model fitting.
Strengths
- Coefficients and predictions remain interpretable in original units
- Flexible extensions support interactions and nonlinear terms
Limitations
- Omitted variables and poor functional form bias interpretation
- High collinearity makes individual coefficients unstable
Know the boundary
Including controls does not itself remove confounding; prediction accuracy and causal identification are separate objectives.