### 15.13 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.