10.3 Roadmap

Rearview Mirror

• Statisticians create a population model to represent the world.

• The BLP is a useful way to summarize the relationship between one outcome random variable \(Y\) and input random varibles \(X_1,...,X_k\)

• OLS regression is an estimator for the Best Linear Predictor (BLP)

• We can capture the sampling uncertainty in an OLS regression with standard errors, and tests for model parameters.

Today

• The research goal determines the strategy for building a linear model.

• Description means summarizing or representing data in a compact, human-understandable way.

• We will capture complex relationships by transforming data, including using indicator variables and interaction terms.

Looking Ahead

• We will see how model building for explanation is different from building for description.

• The famous Classical Linear Model (CLM) allows us to apply regression to smaller samples.