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REGRESSION (ANALYSIS OR LINE)

Sociologyindex, Sociology Books 2012

Regression is a measure of association between two quantitative variables. This form of statistical test is only possible with interval or ratio data.

If an independent variable and a dependent variable are placed on the two axis of a graph with the actual data then scattered on the graph, it is possible to draw a line through the resulting points in a way that minimizes the distance between the points. The resulting line (which may be straight or curved) is a regression line.

Any particular value for the dependent variable can then be predicted by multiplying the value of independent variable by the regression coefficient (a number which determines the slope of the line).

In genetics, regression is the tendency of parents who are exceptional in respect of some partially inherited character to produce offspring in which this character is closer to the mean value for the general population. Frequently referred to as regression to the mean.

In psychology, regression is the process of returning or a tendency to return to an earlier stage of development through hypnosis, psychoanalysis, mental illness.

On Dummy Variable Regression Analysis - A Description and Illustration of the Method 
Jerry L.L. Miller, Maynard L. Erickson, Department of Sociology University of Arizona 
This paper is concerned with the description of a specialized form of linear regression analysis commonly known as "dummy variable" regression analysis. Efforts are made to show the relationship between "dummy variable" regression analysis and other multivariate analysis techniques with a specific emphasis on the kinds of problems and data that sociologists deal with where "dummy variable" regression analysis is particularly appropriate and useful. Efforts are also made (1) to give illustrations and examples of problems to which this type of multiple-regression analysis might be applied productively; (2) to show how "dummy variable" regression analysis is both similar to and different from other multivariate techniques in terms of the analytical procedures and the kinds of interpretations that are made possible. - smr.sagepub.com/cgi/content/abstract/2/4/409?ck=nck

Confronting Sociological Theory with Data: Regression Analysis, Goodman's Log-Linear Models and Comparative Research - Bernice A. Pescosolido, Jonathan Kelley 
Comparisons are central to sociology and prominent among them are comparisons between the way two variables are related in different contexts (e.g. the present compared to the past, blacks compared to whites, industrial societies compared to agrarian ones). It is crucial, therefore, that analytic techniques used to test for such differences accurately reflect the true situation. A variety of statistical approaches have been used, most notably, ordinary least squares (OLS) regression with dummy variables and interaction terms. Recently, however, Goodman's log-linear procedure has been advocated as a `better' way of dealing with certain types of comparisons and particular models have been widely used. However, there is some question as to their applicability in answering theoretical questions typically posed in comparative sociological research. In this paper, we address this issue. Using a Monte Carlo simulation, we set up a typical but hypothetical set of data that would be appropriate for testing comparative theories of socioeconomic achievement or intergenerational mobility. This allows us to examine the ramifications of choosing particular analytic techniques on the conclusions drawn about theoretical propositions. Following conventions established in the literature, we apply two analytic techniques to the same set of data under a variety of conditions. Specifically, we compare the use of widely applied OLS regression and log-linear models where we set (1) the slope differences and (2) the mean differences in the variables between the contexts to vary. The simulation suggests that the regression procedure is able to pick up differences which would be of theoretical interest to the sociologist while the log-linear procedure, given the particular situation modelled here, does not. This is more likely to occur in those cases where the contexts compared have very different distributions. This does not reflect any problems in the log-linear technique itself. Ordered models are more likely to detect these differences because they are parsimonious with respect to degrees of freedom. However, this is not the only factor, methodological or theoretical, that needs to be considered in the choice of techniques. In particular, the findings alert us to difficulties inherent in testing sociological theories where (1) operationalizations of important concepts can result in very different measures and (2) conventional applications of these techniques fail to provide a valid test of proposed theoretical questions. Focussing on factors which may account for the differences observed, we address issues in the existing debate over the use of log-linear and regression models. We discuss the theoretical questions in stratification research for which log-linear techniques can be a useful tool and those for which it is misleading. Finally, we outline the theoretical and methodological tradeoffs in using each technique and suggest another not commonly employed in sociological research. - soc.sagepub.com/cgi/content/abstract/17/3/359

Path Analysis: Supplementary Procedures 
Keith Hope, Oxford Department of Social and Administrative Studies, Nuffield College 
The first purpose of this paper is to indicate the circumstances in which path coefficients may be accepted as adequate guides to the relative importance of anterior (causal) variables in a path analysis. It is shown that weights in a regression equation may be regarded as indicators of importance, in the sense of determinants of proportions of variance, if the (projection of the) variate defined by the equation coincides with a principal component of the anterior variables. 
The second purpose of the paper is to illustrate the usefulness of employing generalized multiple regression (analysis by canonical correlations) as an aid in the interpretation of a path diagram. 
The discussion is illustrated by reference to the path analysis which appears in `Ability and Achievement' by Professor 0. Dudley Duncan.

Comparison of Multiple Regression and Configural Analysis Techniques for Developing Base Expectancy Tables 
Dean V. Babst, New York State Narcotic Addiction Control Commission B.A. (Political Science), 1946, M.A. (Sociology), 1951, University of Washington 
Don M. Gottfredson, Research Center, National Council on Crime and Delinquency; Director, Uniform Parole Reports 
Kelley B. Ballard, JR, Economic Systems Corporation (ADCO), Washington. D.C., Uniform Parole Reports Project, National Parole Institutes, NCCD, 1966-67 
This study compares two statistical techniques-multiple re gression and configural analysis—used in developing parole pre diction tables, according to their ability to (1) differentiate be tween offenders who violate parole and those who do not, (2) predict violators from among a new group of parolees, and (3) assist administrators and researchers. 
First, experience tables had to be developed and tested for prediction ability. Once their accuracy in predicting had been demonstrated, they could be used as base expectancies because they had the quality of being "expected." As such, they could be used as a yardstick to evaluate correctional programs' ability to reduce these "expected" violation rates. 
The two methods were applied to the same body of data and the results were compared. The data consist of Wisconsin adult male offenders paroled in 1954-57 and in 1958-59. All were followed up for two years while they were on parole. The first group was used to develop the experience tables; the second group was used to test prediction ability. 
The tables were compared for accuracy in predicting through use of the Dc index and for accuracy in differentiating by the J index, measures developed by H. Richard John using Daniel Glaser's data gathered for federal parolees. - jrc.sagepub.com/cgi/content/abstract/5/1/72

Review of Regression Models for Categorical Dependent Variables Using Stata, Second Edition, by Long and Freese
Richard Williams, Department of Sociology, University of Notre Dame
Abstract. This article reviews Regression Models for Categorical Dependent
Variables Using Stata, Second Edition, by Long and Freese. - stata.com/bookstore/pdf/long2-review.pdf 

J. Scott Long andJeremy Freese’s (2003) Regression Models for Categorical Dependent Variables UsingStata, Revised Edition. 

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