Linear Models

A common statistical problem is that of comparing several normal population means when the populations are determined by either a categorical or a numerical index. An observation—a “response”—is modeled as Y_i = μ_i + ∊ _i , where https://s3-euw1-ap-pe-df-pch-content-public-p.s3.eu-west-1.amazonaws.com/9780203738511/4df4ccf3-1638-4800-9f99-08cf2b0c9a17/content/eqn489_1.tif"/> and EY_i = μ_i . In the simplest situations the “error” ∊_i has constant variance: σ ² _i = σ ² and all responses are independent.