-@node REGRESSION, , ONEWAY, Statistics
+@node REGRESSION
+@comment node-name, next, previous, up
@section REGRESSION
+@cindex regression
+@cindex linear 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
+@item The data set contains @math{n} observations of a dependent variable, say
+@math{Y_1,@dots{},Y_n}, and @math{n} observations of one or more explanatory
+variables. Let @math{X_{11}, X_{12}}, @dots{}, @math{X_{1n}} denote the @math{n} observations 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 the kth
explanatory variable.
-@item The dependent variable 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}
-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
+@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 ``noise'' terms with mean zero and 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
+@math{b_0,@dots{},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
* Examples:: Using the REGRESSION procedure.
@end menu
-@node Syntax, Examples, , REGRESSION
+@node Syntax
@subsection Syntax
@vindex REGRESSION
/VARIABLES=var_list
/DEPENDENT=var_list
/STATISTICS=@{ALL, DEFAULTS, R, COEFF, ANOVA, BCOV@}
- /EXPORT ('file-name')
+ /SAVE=@{PRED, RESID@}
@end display
The @cmd{REGRESSION} procedure reads the active file and outputs
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
+model. The DEPENDENT subcommand 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.
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
-'file-name' 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
+The SAVE subcommand causes PSPP to save the residuals or predicted
+values from the fitted
+model to the active file. PSPP will store the residuals in a variable
+called RES1 if no such variable exists, RES2 if RES1 already exists,
+RES3 if RES1 and RES2 already exist, etc. It will choose the name of
+the variable for the predicted values similarly, but with PRED as a
+prefix.
+
+@node Examples
@subsection Examples
-The following PSPP code will generate the default output, and save the
-linear model in a program called ``model.c.''
+The following PSPP syntax will generate the default output and save the
+predicted values and residuals to the active file.
@example
title 'Demonstrate REGRESSION procedure'.
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);
+regression /variables=v0 v1 v2 /statistics defaults /dependent=v2
+ /save pred resid /method=enter.
@end example
-
-The file model.c contains the definitions of the functions.
-@setfilename ignored
projects / pspp-builds.git / blobdiff