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.VE $Header: /usr/s/current/s/.help/RCS/regress,v 1.5 87/01/15 19:39:42 rab Exp $
.FN regress
.FN regprt
.TL
regress regprt: Regression Printing
.CS
regress(x, y, wt, int, print, names, ynames, q, correlation)
regprt(regstr, names, ynames, correlation)
.PP
The functions `regress' and `regprt' are related to the `reg'
function, since they print a formatted result of the regression.
`regress(...)' is equivalent to `regprt(reg(...))'.
`regprt' takes
the structure produced by `reg' and prints a summary of the regression
statistics.  `regress' and `regprt' can take vectors of names to augment
the printing of the regression summary.
.PP
See `reg' for details about other arguments to `regress' and `regprt'.
.EX
regress(stack.x,stack.loss,names=stack.collab)
.ft CW
.ps -3
.vs -3

                               Coef       Std Err   t Value
Intercept                  -39.91967    11.89599     -3.35
air flow                     0.7156403   0.1348582    5.30
cooling water inlet temp     1.295286    0.3680243    3.51
acid concentration          -0.1521226   0.1562940   -0.97

N = 21
Residual Standard Error = 3.243364
Multiple R-Square = 0.913577
F Value = 59.9022 on 3, 17 df

Covariance matrix of coefficients:
                            Intercept     air flow
Intercept                   141.5147
air flow                      0.287587   0.01818673
cooling water inlet temp     -0.651794  -0.03651067
acid concentration           -1.676321  -0.00714352

                           cooling water inlet temp
cooling water inlet temp              0.1354418
acid concentration                    0.00001047646

                           acid concentration
acid concentration                 0.02442783

Correlation matrix of coefficients:
                            Intercept   air flow
air flow                    0.1792632
cooling water inlet temp   -0.1488789  -0.7356413
acid concentration         -0.9015999  -0.3389164

                           cooling water inlet temp
acid concentration                      0.000182136
.ps +3
.vs +3
.ft 1
.PP
An explanation of some of the printed statistics:
"Coef", "Std Err", and "t Value" are the coefficients of the regression,
the standard errors of the coefficients,
and the t-value on 17 degrees of freedom
(printed to two decimal places)
for the hypothesis that the coefficient is zero.
"N" is the total number of observations.
"Residual Standard Error" is the square root
of the error variance, the sum of squared residuals divided by
the degrees of freedom for the residuals.
"Multiple R-Square" is the fraction of the variance of `y' explained by the
non-intercept terms of the model.
(If no intercept was fit, this is the fraction of the sum of squares of `y'
explained by the model. 
Unlike the case with an intercept, `y' is not corrected for its mean, and
thus a regression without an intercept can generate multiple r-square
values larger than the corresponding regression with intercept.)
"F Value on n, d df" is the F-test for significance of the whole regression,
where `n' is the number of degrees of freedom for the numerator
(the regression),
and `d' is the number of degrees of freedom for the denominator
(the residuals).
"Covariance and Correlation matrix of coefficients"
give the variances and covariances of the coefficients, and correlations
between the coefficients.
.SH REFERENCE
Norman Draper and Harry Smith,
.ul
Applied Regression Analysis,
Second Edition, Wiley, 1981.
.KW array*
.KW regression
.WR
