5 @cindex linear regression
6 The @cmd{REGRESSION} procedure fits linear models to data via least-squares
7 estimation. The procedure is appropriate for data which satisfy those
8 assumptions typical in linear regression:
11 @item The data set contains @math{n} observations of a dependent variable, say
12 @math{Y_1,@dots{},Y_n}, and @math{n} observations of one or more explanatory
14 Let @math{X_{11}, X_{12}}, @dots{}, @math{X_{1n}} denote the @math{n} observations
15 of the first explanatory variable;
16 @math{X_{21}},@dots{},@math{X_{2n}} denote the @math{n} observations of the second
18 @math{X_{k1}},@dots{},@math{X_{kn}} denote the @math{n} observations of
19 the @math{k}th explanatory variable.
21 @item The dependent variable @math{Y} has the following relationship to the
22 explanatory variables:
23 @math{Y_i = b_0 + b_1 X_{1i} + ... + b_k X_{ki} + Z_i}
24 where @math{b_0, b_1, @dots{}, b_k} are unknown
25 coefficients, and @math{Z_1,@dots{},Z_n} are independent, normally
26 distributed @dfn{noise} terms with mean zero and common variance.
27 The noise, or @dfn{error} terms are unobserved.
28 This relationship is called the @dfn{linear model}.
31 The @cmd{REGRESSION} procedure estimates the coefficients
32 @math{b_0,@dots{},b_k} and produces output relevant to inferences for the
36 * Syntax:: Syntax definition.
37 * Examples:: Using the REGRESSION procedure.
46 /VARIABLES=@var{var_list}
47 /DEPENDENT=@var{var_list}
48 /STATISTICS=@{ALL, DEFAULTS, R, COEFF, ANOVA, BCOV@}
52 The @cmd{REGRESSION} procedure reads the active dataset and outputs
53 statistics relevant to the linear model specified by the user.
55 The @subcmd{VARIABLES} subcommand, which is required, specifies the list of
56 variables to be analyzed. Keyword @subcmd{VARIABLES} is required. The
57 @subcmd{DEPENDENT} subcommand specifies the dependent variable of the linear
58 model. The @subcmd{DEPENDENT} subcommand is required. All variables listed in
59 the @subcmd{VARIABLES} subcommand, but not listed in the @subcmd{DEPENDENT} subcommand,
60 are treated as explanatory variables in the linear model.
62 All other subcommands are optional:
64 The @subcmd{STATISTICS} subcommand specifies the statistics to be displayed:
68 All of the statistics below.
70 The ratio of the sums of squares due to the model to the total sums of
71 squares for the dependent variable.
73 A table containing the estimated model coefficients and their standard errors.
75 Analysis of variance table for the model.
77 The covariance matrix for the estimated model coefficients.
80 The @subcmd{SAVE} subcommand causes @pspp{} to save the residuals or predicted
81 values from the fitted
82 model to the active dataset. @pspp{} will store the residuals in a variable
83 called RES1 if no such variable exists, RES2 if RES1 already exists,
84 RES3 if RES1 and RES2 already exist, etc. It will choose the name of
85 the variable for the predicted values similarly, but with PRED as a
90 The following @pspp{} syntax will generate the default output and save the
91 predicted values and residuals to the active dataset.
94 title 'Demonstrate REGRESSION procedure'.
95 data list / v0 1-2 (A) v1 v2 3-22 (10).
109 regression /variables=v0 v1 v2 /statistics defaults /dependent=v2
110 /save pred resid /method=enter.