From 93164534747a62449f2a2846d09e940159c5eebc Mon Sep 17 00:00:00 2001 From: Jason Stover Date: Wed, 4 Jan 2006 01:34:24 +0000 Subject: [PATCH] Initial version --- doc/regression.texi | 126 ++++++++++++++++++++++++++++++++++++++++++++ 1 file changed, 126 insertions(+) create mode 100644 doc/regression.texi diff --git a/doc/regression.texi b/doc/regression.texi new file mode 100644 index 00000000..4929d5a4 --- /dev/null +++ b/doc/regression.texi @@ -0,0 +1,126 @@ +@node REGRESSION, , ONEWAY, Statistics +@section 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: + +@itemize @bullet +@item 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. + +@item The dependent variable Y has the following relationship to the +explanatory variables: +@math{Y_i = b_0 + b_1 X_1i + ... + b_k X_ki + Z_i} +where @math{b_0, b_1, ..., b_k} are unknown +coefficients, and @math{Z_1,...,Z_n} are independent, normally +distributed ``noise'' terms with common variance. The noise, or +``error'' terms are unobserved. This relationship is called the +``linear model.'' +@end itemize + +The REGRESSION procedure estimates the coefficients +@math{b_0,...,b_k} and produces output relevant to inferences for the +linear model. + +@c If you add any new commands, then don't forget to remove the entry in +@c not-implemented.texi + +@menu +* Syntax:: Syntax definition. +* Examples:: Using the REGRESSION procedure. +@end menu + +@node Syntax, Examples, , REGRESSION +@subsection Syntax + +@vindex REGRESSION +@display +REGRESSION + /VARIABLES=var_list + /DEPENDENT=var_list + /STATISTICS=@{ALL, DEFAULTS, R, COEFF, ANOVA, BCOV@} + /EXPORT (filename) +@end display + +The @cmd{REGRESSION} procedure reads the active file and outputs +statistics relevant to the linear model specified by the user. + +The VARIABLES subcommand, which is required, specifies the list of +variables to be analyzed. Keyword VARIABLES is required. The +DEPENDENT subcommand specifies the dependent variable of the linear +model. The DEPENDENT subcommond is required. All variables listed in +the VARIABLES subcommand, but not listed in the DEPENDENT subcommand, +are treated as explanatory variables in the linear model. + +All other subcommands are optional: + +The STATISTICS subcommand specifies the statistics to be displayed: + +@table @code +@item ALL +All of the statistics below. +@item R +The ratio of the sums of squares due to the model to the total sums of +squares for the dependent variable. +@item COEFF +A table containing the estimated model coefficients and their standard errors. +@item ANOVA +Analysis of variance table for the model. +@item BCOV +The covariance matrix for the estimated model coefficients. +@end table + +The EXPORT subcommand causes PSPP to write a C program containing +functions related to the model. One such function accepts values of +explanatory variables as arguments, and returns an estimate of the +corresponding new +value of the dependent variable. The generated program will also contain +functions that return prediction and confidence intervals related to +those new estimates. PSPP will write the program to the +'filename' given by the user, and write declarations of functions +to a file called pspp_model_reg.h. The user can then compile the C +program and use it as part of another program. This subcommand is a +PSPP extension. + +@node Examples, , Syntax, REGRESSION +@subsection Examples +The following PSPP code will generate the default output, and save the +linear model in a program called ``model.c.'' + +@example +title 'Demonstrate REGRESSION procedure'. +data list / v0 1-2 (A) v1 v2 3-22 (10). +begin data. +b 7.735648 -23.97588 +b 6.142625 -19.63854 +a 7.651430 -25.26557 +c 6.125125 -16.57090 +a 8.245789 -25.80001 +c 6.031540 -17.56743 +a 9.832291 -28.35977 +c 5.343832 -16.79548 +a 8.838262 -29.25689 +b 6.200189 -18.58219 +end data. +list. +regression /variables=v0 v1 v2 /statistics defaults /dependent=v2 /export (model.c) /method=enter. +@end example + +The file pspp_model_reg.h contains these declarations: + +@example +double pspp_reg_estimate (const double *, const char *[]); +double pspp_reg_variance (const double *var_vals, const char *[]); +double pspp_reg_confidence_interval_U (const double *var_vals, const char *var_names[], double p); +double pspp_reg_confidence_interval_L (const double *var_vals, const char *var_names[], double p); +double pspp_reg_prediction_interval_U (const double *var_vals, const char *var_names[], double p); +double pspp_reg_prediction_interval_L (const double *var_vals, const char *var_names[], double p); +@end example + +The file model.c contains the definitions of the functions. +@setfilename ignored -- 2.30.2