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The REG Procedure |

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*label:*>**MODEL***dependents=<regressors> < / options >***;**

Table 55.2 lists the options available in the MODEL statement. Equations for the statistics available are given in the "Model Fit and Diagnostic Statistics" section.

Option |
Description |

Model Selection and Details of Selection | |

SELECTION= | specifies model selection method |

BEST= | specifies maximum number of subset models displayed or output to the OUTEST= data set |

DETAILS | produces summary statistics at each step |

DETAILS= | specifies the display details for forward, backward, and stepwise methods |

GROUPNAMES= | provides names for groups of variables |

INCLUDE= | includes first n variables in the model |

MAXSTEP= | specifies maximum number of steps that may be performed |

NOINT | fits a model without the intercept term |

PCOMIT= | performs incomplete principal component analysis and outputs estimates to the OUTEST= data set |

SLE= | sets criterion for entry into model |

RIDGE= | performs ridge regression analysis and outputs estimates to the OUTEST= data set |

SLS= | sets criterion for staying in model |

START= | specifies number of variables in model to begin the comparing and switching process |

STOP= | stops selection criterion |

Fit Statistics | |

ADJRSQ | computes adjusted R^{2} |

AIC | computes Akaike's information criterion |

B | computes parameter estimates for each model |

BIC | computes Sawa's Bayesian information criterion |

CP | computes Mallows' C_{p} statistic |

GMSEP | computes estimated MSE of prediction assuming multivariate normality |

JP | computes J_{p}, the final prediction error |

MSE | computes MSE for each model |

PC | computes Amemiya's prediction criterion |

RMSE | displays root MSE for each model |

SBC | computes the SBC statistic |

SP | computes S_{p} statistic for each model |

SSE | computes error sum of squares for each model |

Data Set Options | |

EDF | outputs the number of regressors, the error degrees of
freedom, and the model R to the OUTEST= data set^{2} |

OUTSEB | outputs standard errors of the parameter estimates to the OUTEST= data set |

OUTSTB | outputs standardized parameter estimates to the OUTEST= data set. Use only with the RIDGE= or PCOMIT= option. |

OUTVIF | outputs the variance inflation factors to the OUTEST= data set. Use only with the RIDGE= or PCOMIT= option. |

PRESS | outputs the PRESS statistic to the OUTEST= data set |

RSQUARE | has same effect as the EDF option |

Regression Calculations | |

I | displays inverse of sums of squares and crossproducts |

XPX | displays sums-of-squares and crossproducts matrix |

Details on Estimates | |

ACOV | displays asymptotic covariance matrix of estimates assuming heteroscedasticity |

COLLIN | produces collinearity analysis |

COLLINOINT | produces collinearity analysis with intercept adjusted out |

CORRB | displays correlation matrix of estimates |

COVB | displays covariance matrix of estimates |

PCORR1 | displays squared partial correlation coefficients using Type I sums of squares |

PCORR2 | displays squared partial correlation coefficients using Type II sums of squares |

SCORR1 | displays squared semi-partial correlation coefficients using Type I sums of squares |

SCORR2 | displays squared semi-partial correlation coefficients using Type II sums of squares |

SEQB | displays a sequence of parameter estimates during selection process |

SPEC | tests that first and second moments of model are correctly specified |

SS1 | displays the sequential sums of squares |

SS2 | displays the partial sums of squares |

STB | displays standardized parameter estimates |

TOL | displays tolerance values for parameter estimates |

VIF | computes variance-inflation factors |

Predicted and Residual Values | |

CLB | computes % confidence limits for the parameter estimates |

CLI | computes % confidence limits for an individual predicted value |

CLM | computes % confidence limits for the expected value of the dependent variable |

DW | computes a Durbin-Watson statistic |

INFLUENCE | computes influence statistics |

P | computes predicted values |

PARTIAL | displays partial regression plots for each regressor |

R | produces analysis of residuals |

Display Options and Other Options | |

ALL | requests the following options: ACOV, CLB, CLI, CLM, CORRB, COVB, I, P, PCORR1, PCORR2, R, SCORR1, SCORR2, SEQB, SPEC, SS1, SS2, STB, TOL, VIF, XPX |

ALPHA= | sets significance value for confidence and prediction intervals and tests |

NOPRINT | suppresses display of results |

SIGMA= | specifies the true standard deviation of error term for computing CP and BIC |

SINGULAR= | sets criterion for checking for singularity |

You can specify the following options in the MODEL statement after a slash (/).

**ACOV**-
displays the estimated asymptotic covariance matrix of the
estimates under the hypothesis of heteroscedasticity.
See the section "Testing for Heteroscedasticity" for more information.
**ADJRSQ**-
computes
*R*adjusted for degrees of freedom for each model selected (Darlington 1968; Judge et al. 1980).^{2} **AIC**-
computes Akaike's information criterion for each
model selected (Akaike 1969; Judge et al. 1980).
**ALL**-
requests all these options: ACOV, CLB, CLI, CLM, CORRB,
COVB, I, P, PCORR1, PCORR2, R, SCORR1, SCORR2,
SEQB, SPEC, SS1, SS2, STB, TOL, VIF, and XPX.
**ALPHA=***number*-
sets the significance level used for the construction of
confidence intervals for the current MODEL statement.
The value must be between 0 and 1; the
default value of 0.05 results in 95% intervals.
This option affects the MODEL
options CLB, CLI, and CLM; the OUTPUT statement
keywords LCL, LCLM, UCL, and UCLM; the PLOT statement keywords
LCL., LCLM., UCL., and UCLM.; and the PLOT statement options CONF and PRED.
Specifying this option in the MODEL statement takes precedence
over the ALPHA= option in the PROC REG statement.
**B**-
is used with the RSQUARE,
ADJRSQ, and CP model-selection methods to
compute estimated regression coefficients for each model selected.
**BEST=***n*-
is used with the RSQUARE, ADJRSQ, and CP model-selection methods.
If SELECTION=CP or SELECTION=ADJRSQ is specified, the
BEST= option specifies the maximum number of subset
models to be displayed or output to the OUTEST= data set.
For SELECTION=RSQUARE, the BEST= option requests
the maximum number of subset models for each size.

If the BEST= option is used without the B option (displaying estimated regression coefficients), the variables in each MODEL are listed in order of inclusion instead of the order in which they appear in the MODEL statement.

If the BEST= option is omitted and the number of regressors is less than 11, all possible subsets are evaluated. If the BEST= option is omitted and the number of regressors is greater than 10, the number of subsets selected is, at most, equal to the number of regressors. A small value of the BEST= option greatly reduces the CPU time required for large problems. **BIC**-
computes Sawa's Bayesian information criterion for
each model selected (Sawa 1978; Judge et al. 1980).
**CLB**-
requests the % upper- and lower-confidence
limits for the parameter estimates.
By default, the 95% limits are computed;
the ALPHA= option
in the PROC REG or MODEL statement can be used to change the
-level.
**CLI**-
requests the % upper- and lower-confidence
limits for an individual predicted value.
By default, the 95% limits are computed; the
ALPHA= option
in the PROC REG or MODEL statement can be used to change the
-level.
The confidence limits reflect variation in the error,
as well as variation in the parameter estimates.
See the "Predicted and Residual Values" section and Chapter 3, "Introduction to Regression Procedures,"
for more information.
**CLM**-
displays the % upper- and lower-confidence
limits for the expected value of the dependent
variable (mean) for each observation.
By default, the 95% limits are computed;
the ALPHA=
in the PROC REG or MODEL statement can be used to change the
-level.
This is not a prediction interval (see the CLI option)
because it takes into account only the variation in the
parameter estimates, not the variation in the error term.
See the section "Predicted and Residual Values" and Chapter 3 for more information.
**COLLIN**-
requests a detailed analysis of collinearity among the regressors.
This includes eigenvalues, condition indices, and decomposition
of the variances of the estimates with respect to each
eigenvalue.
See the "Collinearity Diagnostics" section.
**COLLINOINT**-
requests the same analysis as the COLLIN option with the intercept
variable adjusted out rather than included in the diagnostics.
See the "Collinearity Diagnostics" section.
**CORRB**-
displays the correlation matrix of the estimates.
This is the (
**X**'**X**)^{-1}matrix scaled to unit diagonals. **COVB**-
displays the estimated covariance matrix of the estimates.
This matrix is (
**X**'**X**)^{-1}*s*, where^{2}*s*is the estimated mean squared error.^{2} **CP**-
computes Mallows'
*C*_{p}statistic for each model selected (Mallows 1973; Hocking 1976). See the "Criteria Used in Model-Selection Methods" section for a discussion of the use of*C*_{p}. **DETAILS****DETAILS=***name*-
specifies the level
of detail produced when the BACKWARD, FORWARD or STEPWISE
methods are used, where
*name*can be ALL, STEPS or SUMMARY. The DETAILS or DETAILS=ALL option produces entry and removal statistics for each variable in the model building process, ANOVA and parameter estimates at each step, and a selection summary table. The option DETAILS=STEPS provides the step information and summary table. The option DETAILS=SUMMARY produces only the summary table. The default if the DETAILS option is omitted is DETAILS=STEPS. **DW**-
calculates a Durbin-Watson statistic to test whether
or not the errors have first-order autocorrelation.
(This test is appropriate only for time series data.)
The sample autocorrelation of the residuals is also produced.
See the section "Autocorrelation in Time Series Data".
**EDF**-
outputs the number of regressors in the model excluding and including
the intercept, the error degrees of freedom, and the model
*R*to the OUTEST= data set.^{2} **GMSEP**-
computes the estimated mean square error of prediction
assuming that both independent and dependent variables
are multivariate normal (Stein 1960; Darlington 1968).
Note that Hocking's formula (1976, eq. 4.20) contains a
misprint: "
*n*-1" should read "*n*-2.") **GROUPNAMES=***'name1' 'name2' ...*-
provides names for variable groups.
This option is available
only in the BACKWARD, FORWARD, and STEPWISE methods.
The group name can be up to 32 characters.
Subsets of independent variables listed in the MODEL
statement can be designated as variable groups.
This is done by enclosing the appropriate variables in braces.
Variables in the same group are entered into or
removed from the regression model at the same time.
However, if the tolerance of any variable (see the
TOL option) in a group is less than the setting
of the SINGULAR= option, then the variable is not
entered into the model with the rest of its group.
If the GROUPNAMES= option is not used,
then the names GROUP1, GROUP2, ..., GROUP
*n*are assigned to groups encountered in the MODEL statement. Variables not enclosed by braces are used as groups of a single variable.

For example,model y={x1 x2} x3 / selection=stepwise groupnames='x1 x2' 'x3';

As another example,model y={ht wgt age} bodyfat / selection=forward groupnames='htwgtage' 'bodyfat';

**I**-
displays the (
**X**'**X**)^{-1}matrix. The inverse of the crossproducts matrix is bordered by the parameter estimates and SSE matrices. **INCLUDE=***n*-
forces the first
*n*independent variables listed in the MODEL statement to be included in all models. The selection methods are performed on the other variables in the MODEL statement. The INCLUDE= option is not available with SELECTION=NONE. **INFLUENCE**-
requests a detailed analysis of the influence of each
observation on the estimates and the predicted values.
See the "Influence Diagnostics" section for
details.
**JP**-
computes
*J*_{p}, the estimated mean square error of prediction for each model selected assuming that the values of the regressors are fixed and that the model is correct. The*J*_{p}statistic is also called the final prediction error (FPE) by Akaike (Nicholson 1948; Lord 1950; Mallows 1967; Darlington 1968; Rothman 1968; Akaike 1969; Hocking 1976; Judge et al. 1980). **MSE**-
computes the mean square error for
each model selected (Darlington 1968).
**MAXSTEP=***n*-
specifies the maximum number of steps that are done when
SELECTION=FORWARD, SELECTION=BACKWARD or SELECTION=STEPWISE is used. The default value
is the number of independent variables in the model
for the forward and backward methods and three times this number
for the stepwise method.
**NOINT**-
suppresses the intercept term that
is otherwise included in the model.
**NOPRINT**-
suppresses the normal display of regression results.
Note that this option
temporarily disables the Output Delivery System (ODS);
see Chapter 15, "Using the Output Delivery System," for more information.
**OUTSEB**-
outputs the standard errors of the parameter estimates to
the OUTEST= data set. The value SEB for the variable _TYPE_
identifies the standard errors. If the RIDGE= or PCOMIT= option is
specified, additional observations are included and identified by
the values RIDGESEB and IPCSEB, respectively, for the
variable _TYPE_.
The standard errors for ridge regression estimates and
incomplete principal components (IPC) estimates are limited in their usefulness because these
estimates are biased. This option is available for all model-selection
methods except RSQUARE, ADJRSQ, and CP.
**OUTSTB**-
outputs the standardized parameter estimates as well as the
usual estimates to the OUTEST= data set when the RIDGE= or
PCOMIT= option is specified. The values RIDGESTB and IPCSTB for the
variable _TYPE_ identify ridge regression estimates and IPC
estimates, respectively.
**OUTVIF**-
outputs the variance inflation factors (VIF)
to the OUTEST= data set when the RIDGE= or PCOMIT= option
is specified. The factors are the diagonal elements of the inverse
of the correlation
matrix of regressors as adjusted by ridge regression or IPC
analysis. These observations are identified in the output
data set by the values RIDGEVIF and IPCVIF for the variable
_TYPE_.
**P**-
calculates predicted values from the
input data and the estimated model.
The display includes the observation number,
the ID variable (if one is specified), the
actual and predicted values, and the residual.
If the CLI, CLM, or R option is specified, the P option is unnecessary.
See the section "Predicted and Residual Values" for more information.
**PARTIAL**-
requests partial regression leverage plots for each regressor.
See the "Influence Diagnostics" section for more information.
**PC**-
computes Amemiya's prediction criterion for each
model selected (Amemiya 1976; Judge et al. 1980).
**PCOMIT=***list*-
requests an IPC analysis for each
value
*m*in the list. The procedure computes parameter estimates using all but the last*m*principal components. Each value of*m*produces a set of IPC estimates, which is output to the OUTEST= data set. The values of*m*are saved by the variable _PCOMIT_, and the value of the variable _TYPE_ is set to IPC to identify the estimates. Only nonnegative integers can be specified with the PCOMIT= option.

If you specify the PCOMIT= option, RESTRICT statements are ignored. The PCOMIT= option is ignored if you use the SELECTION= option in the MODEL statement. **PCORR1**-
displays the squared partial correlation
coefficients using Type I Sum of Squares (SS).
This is calculated as SS/(SS+SSE),
where SSE is the error Sum of Squares.
**PCORR2**-
displays the squared partial correlation
coefficients using Type II sums of squares.
These are calculated the same way as with the PCORR1 option, except
that Type II SS are used instead of Type I SS.
**PRESS**-
outputs the PRESS statistic to the OUTEST= data set.
The values of this statistic are saved in the variable _PRESS_.
This option is available for all model-selection methods except
RSQUARE, ADJRSQ, and CP.
**R**-
requests an analysis of the residuals.
The results include everything requested by the P option
plus the standard errors of the mean predicted and residual values,
the studentized residual, and Cook's
*D*statistic to measure the influence of each observation on the parameter estimates. See the section "Predicted and Residual Values" for more information. **RIDGE=***list*-
requests a ridge regression analysis and specifies the values of the
ridge constant
*k*(see the "Computations for Ridge Regression and IPC Analysis" section). Each value of*k*produces a set of ridge regression estimates that are placed in the OUTEST= data set. The values of*k*are saved by the variable _RIDGE_, and the value of the variable _TYPE_ is set to RIDGE to identify the estimates.

Only nonnegative numbers can be specified with the RIDGE= option. Example 55.10 illustrates this option.

If you specify the RIDGE= option, RESTRICT statements are ignored. The RIDGE= option is ignored if you use the SELECTION= option in the MODEL statement. **RMSE**-
displays the root mean square error for each model selected.
**RSQUARE**-
has the same effect as the EDF option.
**SBC**-
computes the SBC statistic for each model
selected (Schwarz 1978; Judge et al. 1980).
**SCORR1**-
displays the squared semi-partial correlation
coefficients using Type I sums of squares.
This is calculated as SS/SST, where
SST is the corrected total SS.
If the NOINT option is used, the uncorrected
total SS is used in the denominator.
**SCORR2**-
displays the squared semi-partial correlation
coefficients using Type II sums of squares.
These are calculated the same way as with the SCORR1 option, except
that Type II SS are used instead of Type I SS.
**SELECTION=***name*-
specifies the method used to select the model, where
*name*can be FORWARD (or F), BACKWARD (or B), STEPWISE, MAXR, MINR, RSQUARE, ADJRSQ, CP, or NONE (use the full model). The default method is NONE. See the "Model-Selection Methods" section for a description of each method. **SEQB**-
produces a sequence of parameter estimates
as each variable is entered into the model.
This is displayed
as a matrix where each
row is a set of parameter estimates.
**SIGMA=***n*-
specifies the true standard deviation of the error
term to be used in computing the CP
and BIC statistics.
If the SIGMA= option is not specified,
an estimate from the full model is used.
This option is available in the RSQUARE,
ADJRSQ, and CP model-selection methods only.
**SINGULAR=***n*-
tunes the mechanism used to check for singularities.
Specifying this option in the MODEL statement takes precedence
over the SINGULAR= option in the PROC REG statement.
The default value is machine dependent but is approximately 1E-7 on
most machines. This option is rarely needed.
Singularity checking is described in
the "Computational Methods" section.
**SLENTRY=***value***SLE=***value*-
specifies the significance level for entry into
the model used in the FORWARD and STEPWISE methods.
The defaults are 0.50 for FORWARD and 0.15 for STEPWISE.
**SLSTAY=***value***SLS=***value*-
specifies the significance level for staying in
the model for the BACKWARD and STEPWISE methods.
The defaults are 0.10 for BACKWARD and 0.15 for STEPWISE.
**SP**-
computes the
*S*_{p}statistic for each model selected (Hocking 1976). **SPEC**-
performs a test that the first and second
moments of the model are correctly specified.
See the section "Testing for Heteroscedasticity" for more information.
**SS1**-
displays the sequential sums of squares (Type I SS) along
with the parameter estimates for each term in the model.
See Chapter 12, "The Four Types of Estimable Functions,"
for more
information on the different types of sums of squares.
**SS2**-
displays the partial sums of squares (Type II SS) along
with the parameter estimates for each term in the model.
See the SS1 option also.
**SSE**-
computes the error sum of squares for each model selected.
**START=***s*-
is used to begin the comparing-and-switching process
in the MAXR, MINR, and STEPWISE methods for a model
containing the first
*s*independent variables in the MODEL statement, where*s*is the START value. For these methods, the default is START=0.

For the RSQUARE, ADJRSQ, and CP methods, START=*s*specifies the smallest number of regressors to be reported in a subset model. For these methods, the default is START=1.

The START= option cannot be used with model-selection methods other than the six described here. **STB**-
produces standardized regression coefficients.
A standardized regression coefficient is computed
by dividing a parameter estimate by the ratio of the
sample standard deviation of the dependent variable
to the sample standard deviation of the regressor.
**STOP=***s*-
causes PROC REG to stop when it has found the "best"
*s*-variable model, where*s*is the STOP value. For the RSQUARE, ADJRSQ, and CP methods, STOP=*s*specifies the largest number of regressors to be reported in a subset model. For the MAXR and MINR methods, STOP=*s*specifies the largest number of regressors to be included in the model.

The default setting for the STOP= option is the number of variables in the MODEL statement. This option can be used only with the MAXR, MINR, RSQUARE, ADJRSQ and CP methods. **TOL**-
produces tolerance values for the estimates.
Tolerance for a variable is defined as 1-
*R*, where^{2}*R*is obtained from the regression of the variable on all other regressors in the model. See the section "Collinearity Diagnostics" for more detail.^{2} **VIF**-
produces variance inflation factors with the parameter estimates.
Variance inflation is the reciprocal of tolerance.
See the section "Collinearity Diagnostics" for more detail.
**XPX**-
displays the
**X**'**X**crossproducts matrix for the model. The crossproducts matrix is bordered by the**X**'**Y**and**Y**'**Y**matrices.

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