REGRESS(1)                         |STAT                   January 27, 1987

NAME
     regress - multivariate linear regression and correlation

SYNOPSIS
     regress [-ceprs] [column names]

DESCRIPTION
     _r_e_g_r_e_s_s performs a general linear correlation and regression analysis
     for up to 20 variables.  Input is a series of lines, each containing
     an equal number of numerical fields.  Names for these fields can be
     supplied, but if none are given, REG, A, B, C, etc. are used.

     For regression analysis, the first column is predicted with all the
     others (see _d_m or _c_o_l_e_x to reorder columns).

OPTIONS
     -c   Print the covariance matrix.

     -e   Save the regression equation in the file _r_e_g_r_e_s_s._e_q_n. This file
          is designed for use with the data manipulator _d_m. Suppose the
          input to _r_e_g_r_e_s_s is in _r_e_g_r_e_s_s._i_n. Then,
                               regress -e < regress.in
          can be followed by
                       dm Eregress.eqn < regress.in | pair -p
          to plot the obtained against the predicted values.  The residuals
          can be obtained with an extra pass through _d_m:
           dm  Eregress.eqn  <  regress.in  |  dm  x2  x1-x2  |  pair  -p

     -p   Do a partial correlation analysis to determine the contribution
          of individual predictors after the others have been included.
          _r_e_g_r_e_s_s reports, for each predictor, the regression weight (b)
          and the standardized regression weight (beta).  The Rsq value is
          the squared multiple correlation of the predictor with all other
          predictors; if there is only one predictor, this will be zero,
          and if there is only one other, both Rsq's will be identical.
          Also reported is the standard error of the regression weight (b).
          The significance test answers the question: ``After all the other
          variables have been taken into account, does this variable
          significantly improve prediction?''

     -r   Do no regression analysis.  Only print the correlation matrix and
          summary statistics.

     -s   Print the matrix of raw sums of squares and cross products.

DIAGNOSTICS
     _r_e_g_r_e_s_s will complain about a singular correlation matrix if variables
     are perfectly correlated.

ALGORITHM
     Chapter 4 of Kerlinger and Pedhazur (1973) _M_u_l_t_i_p_l_e _R_e_g_r_e_s_s_i_o_n _i_n
     _B_e_h_a_v_i_o_r_a_l _R_e_s_e_a_r_c_h. New York: Holt, Rinehart & Winston.

LIMITS
     Use the -L option to determine the program limits.

MISSING VALUES
     Cases with missing data values (NA) are counted but not included in
     the analysis.
