### 15.17 REGRESSION ¶

The `REGRESSION` procedure fits linear models to data via least-squares estimation. The procedure is appropriate for data which satisfy those assumptions typical in linear regression:

- The data set contains n observations of a dependent variable, say Y_1,...,Y_n, and n observations of one or more explanatory variables. Let X_{11}, X_{12}, …, X_{1n} denote the n observations of the first explanatory variable; X_{21},…,X_{2n} denote the n observations of the second explanatory variable; X_{k1},…,X_{kn} denote the n observations of the kth explanatory variable.
- The dependent variable Y has the following relationship to the explanatory variables: Y_i = b_0 + b_1 X_{1i} + ... + b_k X_{ki} + Z_i where b_0, b_1, ..., b_k are unknown coefficients, and Z_1,...,Z_n are independent, normally distributed noise terms with mean zero and common variance. The noise, or error terms are unobserved. This relationship is called the linear model.

The `REGRESSION` procedure estimates the coefficients b_0,...,b_k and produces output relevant to inferences for the linear model.