+@c PSPP - a program for statistical analysis.
+@c Copyright (C) 2017, 2020 Free Software Foundation, Inc.
+@c Permission is granted to copy, distribute and/or modify this document
+@c under the terms of the GNU Free Documentation License, Version 1.3
+@c or any later version published by the Free Software Foundation;
+@c with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts.
+@c A copy of the license is included in the section entitled "GNU
+@c Free Documentation License".
+@c
@node REGRESSION
@section REGRESSION
of the first explanatory variable;
@math{X_{21}},@dots{},@math{X_{2n}} denote the @math{n} observations of the second
explanatory variable;
-@math{X_{k1}},@dots{},@math{X_{kn}} denote the @math{n} observations of
+@math{X_{k1}},@dots{},@math{X_{kn}} denote the @math{n} observations of
the @math{k}th explanatory variable.
-@item The dependent variable @math{Y} has the following relationship to the
+@item The dependent variable @math{Y} has the following relationship to the
explanatory variables:
-@math{Y_i = b_0 + b_1 X_{1i} + ... + b_k X_{ki} + Z_i}
+@math{Y_i = b_0 + b_1 X_{1i} + ... + b_k X_{ki} + Z_i}
where @math{b_0, b_1, @dots{}, b_k} are unknown
coefficients, and @math{Z_1,@dots{},Z_n} are independent, normally
distributed @dfn{noise} terms with mean zero and common variance.
The @cmd{REGRESSION} procedure estimates the coefficients
@math{b_0,@dots{},b_k} and produces output relevant to inferences for the
-linear model.
+linear model.
@menu
* Syntax:: Syntax definition.
REGRESSION
/VARIABLES=@var{var_list}
/DEPENDENT=@var{var_list}
- /STATISTICS=@{ALL, DEFAULTS, R, COEFF, ANOVA, BCOV, CI[@var{conf}]@}
+ /STATISTICS=@{ALL, DEFAULTS, R, COEFF, ANOVA, BCOV, CI[@var{conf}, TOL]@}
+ @{ /ORIGIN | /NOORIGIN @}
/SAVE=@{PRED, RESID@}
@end display
All other subcommands are optional:
-The @subcmd{STATISTICS} subcommand specifies additional statistics to be displayed.
+The @subcmd{STATISTICS} subcommand specifies which statistics are to be displayed.
The following keywords are accepted:
@table @subcmd
Analysis of variance table for the model.
@item BCOV
The covariance matrix for the estimated model coefficients.
+@item TOL
+The variance inflation factor and its reciprocal. This has no effect unless COEFF is also given.
@item DEFAULT
The same as if R, COEFF, and ANOVA had been selected.
+This is what you get if the /STATISTICS command is not specified,
+or if it is specified without any parameters.
@end table
+The @subcmd{ORIGIN} and @subcmd{NOORIGIN} subcommands are mutually
+exclusive. @subcmd{ORIGIN} indicates that the regression should be
+performed through the origin. You should use this option if, and
+only if you have reason to believe that the regression does indeed
+pass through the origin --- that is to say, the value @math{b_0} above,
+is zero. The default is @subcmd{NOORIGIN}.
+
The @subcmd{SAVE} subcommand causes @pspp{} to save the residuals or predicted
values from the fitted
model to the active dataset. @pspp{} will store the residuals in a variable
-called @samp{RES1} if no such variable exists, @samp{RES2} if @samp{RES1}
+called @samp{RES1} if no such variable exists, @samp{RES2} if @samp{RES1}
already exists,
@samp{RES3} if @samp{RES1} and @samp{RES2} already exist, etc. It will
choose the name of
b 6.200189 -18.58219
end data.
list.
-regression /variables=v0 v1 v2 /statistics defaults /dependent=v2
+regression /variables=v0 v1 v2 /statistics defaults /dependent=v2
/save pred resid /method=enter.
@end example