Regression Analysis
The SAS/STAT regression analysis procedures include the following:
NLIN Procedure
The NLIN procedure fits nonlinear regression models and estimates the parameters by nonlinear least squares or weighted nonlinear
least squares. You specify the model with programming statements. This gives you great flexibility in modeling the relationship
between the response variable and independent (regressor) variables. It does, however, require additional coding compared to model
specifications in linear modeling procedures such as the REG, GLM, and MIXED procedures. The following are highlights of the NLIN
procedure's features:
 provides a highquality automatic differentiator so that you do not need to specify first and second derivatives. You can, however, specify the derivatives if you wish.
 solves the nonlinear least squares problem by one of the following four algorithms (methods):
 steepestdescent or gradient method
 Newton method
 modified GaussNewton method
 Marquardt method
 enables you to confine the estimation procedure to a certain range of values of the parameters by imposing bounds on the estimates
 computes Hougaard's measure of skewness

 provides bootstrap estimates of confidence intervals for parameters and the covariance/correlation matrices of the parameter estimates
 performs weighted estimation
 creates an output data set that contains statistics that are calculated for each observation
 creates a data set that contains the parameter estimates at each iteration
 performs BY group processing, which enables you to obtain separate analyses on grouped observations
 creates a SAS data set that corresponds to any output table
 automatically created graphs by using ODS Graphics

For further details, see
NLIN Procedure
ORTHOREG Procedure
The ORTHOREG procedure fits general linear models by the method of least squares. Other SAS/STAT software procedures, such
as the GLM and REG procedures, fit the same types of models, but PROC ORTHOREG can produce more accurate estimates than other
regression procedures when your data are illconditioned. The following are highlights of the ORTHOREG procedure's features:
 uses GentlemanGivens transformations to update and compute the upper triangular matrix R of the QR decomposition of the data matrix
 enables you to construct special collections of columns for design matrices
 produces a display of the fitted model and provides options for changing and enhancing the displays
 enables you to perform F tests for model effects that test Type I, Type II, or Type III hypotheses
 enables you to obtain custom hypothesis tests
 computes and compares least squares means (LSmeans) of fixed effects

 provides a general mechanism for performing a partitioned analysis of the LSmeans for an interaction
 enables you to save the context and results of the statistical analysis in an item store, which can be processed by the PLM procedure
 performs weighted estimation
 performs BY group processing, which enables you to obtain separate analyses on grouped observations
 creates SAS data sets for analysis of variance, fit statistics, table of class variables, and parameter estimates

For further details, see
ORTHOREG Procedure
PLM Procedure
The PLM procedure performs postfitting statistical analyses for the contents of a SAS item store that was previously
created with the STORE statement in some other SAS/STAT procedure. An item store is a special SASdefined binary file format
used to store and restore information with a hierarchical structure.
The following are highlights of the PLM procedure's features:
 performs custom hypothesis tests
 computes confidence intervals
 produces prediction plots
 scores a new data set
 enables you to filter the results

 offers the most advanced postprocessing techniques available in SAS/STAT including the following:
 stepdown multiplicity adjustments for pvalues
 F tests with order restrictions
 analysis of means (ANOM)
 samplingbased linear inference based on Bayes posterior estimates

For further details, see
PLM Procedure
PLS Procedure
The PLS procedure fits models by using any one of a number of linear predictive methods including partial least squares (PLS).
Ordinary least squares regression, as implemented in SAS/STAT procedures such as PROC GLM and PROC REG, has the single goal of
minimizing sample response prediction error, seeking linear functions of the predictors that explain as much variation in each response as possible.
The techniques implemented in the PLS procedure have the additional goal of accounting for variation in the predictors, under the
assumption that directions in the predictor space that are well sampled should provide better prediction for new observations when
the predictors are highly correlated. All of the techniques implemented in the PLS procedure work by extracting successive linear
combinations of the predictors, called factors (also called components, latent vectors, or latent variables), which optimally address
one or both of these two goals—explaining response variation and explaining predictor variation. In particular, the method of partial
least squares balances the two objectives, seeking factors that explain both response and predictor variation.
The following are highlights of the PLS procedure's features:
 implements the following techniques:
 principal components regression, which extracts factors to explain as much predictor sample variation as possible
 reduced rank regression, which extracts factors to explain as much response variation as possible.
This technique, also known as (maximum) redundancy analysis, differs from multivariate linear regression only when there are multiple responses.
 partial least squares regression, which balances the two objectives of explaining response variation and explaining predictor variation.
Two different formulations for partial least squares are available: the original predictive method of Wold (1966) and the SIMPLS method of de Jong (1993).

 enables you to choose the number of extracted factors by cross validation
 enables you to use the general linear modeling approach of the GLM procedure to specify a model for
your design, allowing for general polynomial effects as well as classification or ANOVA effects
 enables you to save the fitted model in a data set and apply it to new data by using the SCORE procedure
 performs BY group processing, which enables you to obtain separate analyses on grouped observations
 creates an output data set to receive quantities that can be computed for every input observation, such as extracted factors and predicted values
 automatically creates graphs by using ODS Graphics

For further details, see
PLS Procedure
REG Procedure
The REG procedure is a general purpose procedure for ordinary least squares regression. The following
are highlights of the REG procedure's features:
 supports multiple MODEL statements
 provides nine modelselection methods
 allows interactive changes both in the model and the data used to fit the model
 supports linear equality restrictions on parameters
 provides tests of linear hypotheses and multivariate hypotheses
 provides collinearity diagnostics
 computes predicted values, residuals, studentized residuals, confidence limits, and influence statistics

 allows correlation or crossproduct input
 saves requested statistics to SAS data sets
 enables you to save the fitted model to an item store, which can be processed by the PLM procedure
 performs BY group processing, which enables you to obtain separate analyses on grouped observations
 perform weighted estimation
 create a SAS data set that corresponds to any output table
 automatically creates graphs by using ODS Graphics

For further details, see
REG Procedure
RSREG Procedure
The RSREG procedure uses the method of least squares to fit quadratic response surface regression models.
Response surface models are a kind of general linear model in which attention focuses on characteristics
of the fit response function and in particular, where optimum estimated response values occur.
The following are highlights of the RSREG procedure's features:
 performs a lak of fit test
 enables you to test for the significance of individual factors
 enables you to analyze the canonical structure of the estimated response surface
 computes the ridge of optimum response
 predicts new values of the response

 performs BY group processing, which enables you to obtain separate analyses on grouped observations
 performs weighted estimation
 creates a SAS data set that contains statistics for each observation in the input data set
 creates a SAS data set that corresponds to any table
 automatically produces graphs by using ODS Graphics

For further details, see
RSREG Procedure
TRANSREG Procedure
The TRANSREG (transformation regression) procedure fits linear models, optionally with smooth, spline, BoxCox, and other nonlinear
transformations of the variables. The following are highlights of the TRANSREG procedure's features:
 enables you to fit linear models including:
 ordinary regression and ANOVA
 metric and nonmetric conjoint analysis (Green and Wind 1975; de Leeuw, Young, and Takane 1976)
 linear models with BoxCox (1964) transformations of the dependent variables
 regression with a smooth (Reinsch 1967), spline (de Boor 1978; van Rijckevorsel 1982),
monotone spline (Winsberg and Ramsay 1980), or penalized Bspline (Eilers and Marx 1996)
fit function
 metric and nonmetric vector and ideal point preference mapping (Carroll 1972)
 simple, multiple, and multivariate regression with variable transformations (Young,
de Leeuw, and Takane 1976; Winsberg and Ramsay 1980; Breiman and Friedman 1985)
 redundancy analysis (Stewart and Love 1968) with variable transformations (Israels 1984)
 canonical correlation analysis with variable transformations (van der Burg and de Leeuw 1983)
 response surface regression (Meyers 1976; Khuri and Cornell 1987) with variable transformations
 enables you to use a data set that can contain variables measured on nominal, ordinal, interval, and ratio scales;
you can specify any mix of these variable types for the dependent and independent variables
 transform nominal variables by scoring the categories to minimize squared error
(Fisher 1938), or treat nominal variables as classification variables

 enables you to transform ordinal variables by monotonically scoring the ordered categories so that order is
weakly preserved (adjacent categories can be merged) and squared error is minimized. Ties
can be optimally untied or left tied (Kruskal 1964). Ordinal variables can also be transformed
to ranks.
 enables you to transform interval and ratio scale of measurement variables linearly or nonlinearly with spline
(de Boor 1978; van Rijckevorsel 1982), monotone spline (Winsberg and Ramsay 1980),
penalized Bspline (Eilers and Marx 1996), smooth (Reinsch 1967), or BoxCox (Box and
Cox 1964) transformations. In addition, logarithmic, exponential, power, logit, and inverse
trigonometric sine transformations are available.
 fits a curve through a scatter plot or fit multiple curves, one for each level of a classification variable
 enables you to constrain the functions to be parallel or monotone or have the same intercept
 enables you to code experimental designs and classification variables prior to their use in other analyses
 perform sweighted estimation
 generates output data sets including
 ANOVA results
 regression tables
 conjoint analysis partworth utilities
 coefficients
 marginal means
 original and transformed variables, predicted values, residuals, scores, and more
 performs BY group processing, which enables you to obtain separate analyses on grouped observations
 automatically creates graphs by using ODS Graphics

For further details, see
TRANSREG Procedure