REGRESSION 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