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 @samp{RES1} if no such variable exists, @samp{RES2} if @samp{RES1}
85 @samp{RES3} if @samp{RES1} and @samp{RES2} already exist, etc. It will
87 the variable for the predicted values similarly, but with @samp{PRED} as a
89 When @subcmd{SAVE} is used, @pspp{} ignores @cmd{TEMPORARY}, treating
90 temporary transformations as permanent.
94 The following @pspp{} syntax will generate the default output and save the
95 predicted values and residuals to the active dataset.
98 title 'Demonstrate REGRESSION procedure'.
99 data list / v0 1-2 (A) v1 v2 3-22 (10).
113 regression /variables=v0 v1 v2 /statistics defaults /dependent=v2
114 /save pred resid /method=enter.