The SPSS procedure REGRESSION computes ordinary least
squares regression for assessing the effects of one or
more independent variables on a continuous dependent
variable. The regression coefficients for an independent
variable summarize the effects of the independent
variable on the dependent variable when the effects of
the other independent variables included in the
regression analysis are controlled for or held
constant.
Thus, given the complexities of the real world in
which many social phenonmenon are the result of several
factors, multiple regression (two or more independent
variables) is an especially powerful analytic tool for
data analysis.

There are many technical statistical terms associated
with regression analysis of which only a few of the more
important ones will be highlighted here. Students are
encouraged to consult their statistical texts and/or
their SPSS manuals for a more thorough discussion of
regression concepts.

In the multivariate case (two or more independent
variables) the equation for calculating a straight line
is written as follows:

Y = a + B1X1 + B2X2 + B3X3 + e
*Where*: a = the constant (point at
which line crosses Y axis)
B1 = slope (regression coefficeint) for
variable X1
B2 = slope for variable X2

B3 = slope for variable X3

e = error (or residual) value

We add an error term to our regression equation
because the independent variables by themselves cannot
fully account for all the observed variation in the
dependent variable. This error term consists of two
components: the effects on the dependent variable of
independent variables not included in the regression
equation and random or residual variation.

Regression analysis produces **two types of
statistics**. One set of statistics provides
information about the individual independent variables
included in the analysis and summarizes the relationship
between each independent variable and the dependent
variable. A second set of regression statistics provides
information about the regression model as a whole,
summarizing the extent to which all of the variables
included in the regression model explain variation in the
dependent variable.

**Statistics for Independent Variables**

Unstandardized regression coefficient
Standardized regression coefficient (beta
weight)

Significance test for individual regression
coefficients

**Statistics for Regression Equation**

Multiple R , R Square, and Adjusted R Square
Standard Error

Significance test for equation (5 of 12)

SPSS offers several **methods **for regression
model building, four of which will be reviewed here. The
choice of which method to use is ultimately one the
individual researcher must make and should be guided by
one's theoretical understandings regarding the
relationships among the variables included in the
analysis and the purposes of the analysis. Model building
refers to the selection of the most parisminous set of
variables that explain the variation in the dependent
variable. Each of the regression method options is
designed to assist the researcher in identifying this set
of variables. The available methods include:

Forward Selection
Backward Selection

Stepwise Selection

Forced Entry

**Regression Syntax**

At a minimum, the SPSS command for REGRESSION must
include three subcommands: (1) a VARIABLES subcommand
that indentifies the variables to be included in the
analysis, (2) a DEPENDENT subcommand that identifies
which of the variables is to be treated as the dependent
variable, and (3) a METHOD subcommand that specifies
which of the various model-building procedures will be
used for estimating the regression equation. Optional
commands are available that allow the researcher to set
specific entry and/or removal criteria, receive
additional regression and descriptive statistics, and to
conduct several diagnostic procedures involving analysis
of the residuals.

*For example*, to assess the relative
importance of unemployment, poverty, and crime in
explaining the distribution of federal aid to cities
in 1990 using the stepwise method, one would include
the following commands:
REGRESSION
VARIABLES=FEDAID, UNEMP, POVERTY, CRIME
/DEPENDENT=FEDAID

/METHOD=STEPWISE