Roadmap
Rearview Mirror
- Statisticians create a population model to represent the world.
- \(E[X], V[X], Cov[X,Y]\) are “simple” summaries of complex joint distributions, which are hooks for our analyses.
- They also have useful properties – for example, \(E[X + Y] = E[X] + E[Y]\).
This week
- We look at situations with one or more “input” random variables, and one “output.”
- Conditional expectation summarizes the output, given values for the inputs.
- The conditional expectation function (CEF) is a predictor – a function that yields a value for the output, give values for the inputs.
- The best linear predictor (BLP) summarizes a relationship using a line / linear function.
Coming Attractions
- OLS regression is a workhorse of modern statistics, causal analysis, etc
- It is also the basis for many other models in classical stats and machine learning
- The target that OLS estimates is exactly the BLP, which we’re learning about this week.