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*k*th 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.