2 The Two-Variable Linear Model
Section 1 showed that the best linear predictor of \(Y\) given \(X\) always exists and is given by population moments. This section estimates it from a sample, establishes the properties of the estimator under explicit assumptions, and builds the machinery of inference: standard errors, \(t\) tests, confidence intervals and prediction intervals. Everything here is done with sums, so that the ideas are visible without matrix algebra. With the \(k\)-variable model the same results are re-derived in matrix form for any number of regressors, and the two-variable results become special cases.
2.1 The model and its assumptions
2.2 Least squares
2.3 Properties of the least squares estimators
2.4 Inference
2.5 Prediction
2.6 Regression in software
2.7 Practice Problems
2.2 Least squares
2.3 Properties of the least squares estimators
2.4 Inference
2.5 Prediction
2.6 Regression in software
2.7 Practice Problems
Questions on this section
Stuck on something here? Ask below and it stays attached to this topic.