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# Multiple Regression (Statistical Associates Blue Book Series) [Kindle Edition]

G. David Garson

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## Book Description

Overview
Multiple regression, a time-honored technique going back to Pearson's use of it in 1908, is employed to account for (predict) the variance in an interval dependent variable, based on linear combinations of interval, dichotomous, or dummy independent variables. Often called OLS regression because of its reliance on ordinary least squares estimation, multiple regression can establish whether a set of independent variables explains a proportion of the variance in a dependent variable at a significant level (through a significance test of R2), and can establish the relative predictive importance of the independent variables (by comparing beta weights). Power terms can be added as independent variables to explore curvilinear effects. Cross-product terms can be added as independent variables to explore interaction effects. One can test the significance of the difference of two R2's to determine if adding an independent variable to the model would help significantly. Using hierarchical regression, the researcher can see how much variance in the dependent variable can be explained by one or a set of new independent variables, over and above that explained by an earlier set. The parameter estimates (b coefficients and the constant) can be used to construct a prediction equation and generate predicted scores for further analysis.
The multiple regression equation takes the form y = b1x1 + b2x2 + ... + bnxn + c. The b's are the regression coefficients, representing the amount the dependent variable (y) changes when the corresponding independent variable changes 1 unit. The c is the constant, indicating where the regression line intercepts the y axis, representing the magnitude the dependent will be when all the independent variables are held to 0. The standardized version of the b coefficients are the beta weights, and the ratio of the beta coefficients is often interpreted as the ratio of the relative predictive power of the independent variables. Associated with multiple regression is R2, multiple correlation, which is the percent of variance in the dependent variable explained collectively by all of the independent variables in the model.
Multiple regression shares all the assumptions of correlation: linearity of relationships, the same level of relationship throughout the range of the independent variable (homoscedasticity), interval or near-interval measurement level, absence of outliers, and data whose range is not truncated. In addition, it is important that the model being tested is correctly specified. The exclusion of important causal variables or the inclusion of extraneous variables can change markedly the beta weights and hence the interpretation of the importance of the independent variables.
There are many of alternatives to ordinary least squares (OLS) regression, including general linear models, generalized linear models, linear mixed models, logistic regression, Cox regression, and many more. These are treated in separate volumes of the Statistical Associates "blue book" series.

Key Terms and Concepts 13
OLS 13
Variables 13
Regression equation 13
Dependent variable 14
Independent variables 14
Dummy variables 14
Interaction effects 15
Interactions 15
Significance of interaction effects 16
Interaction terms involving categorical dummies 17
Separate regressions 17
Predicted values 18
Predicted values 18
Residuals 19
Centering 19
Regression coefficients in SPSS 20
Example 20
The regression coefficient, b 20
Coefficients table 21
Zero-order, partial, and part correlations 21
Squared partial correlation 22
Semi-partial correlation 22
Interpreting b for dummy variables 22
Regression coefficients in SAS 23
Example 23
SAS syntax 23
SAS tables 24
SAS plots 26
Residual by regressor plots 26
Fit diagnostics panel 27
Residuals vs. predicted values 27
Studentized residuals vs. predicted values 27
Studentized residuals vs. leverage 27

110 more pages of regression topics

## Product Details

• File Size: 2595 KB
• Print Length: 153 pages
• Publisher: Statistical Associates Publishers; 1 edition (May 1, 2012)
• Sold by: Amazon Digital Services, Inc.
• Language: English
• ASIN: B007ZK7MSQ
• Text-to-Speech: Enabled
• X-Ray: Not Enabled
• Lending: Enabled
• Amazon Best Sellers Rank: #250,035 Paid in Kindle Store (See Top 100 Paid in Kindle Store)
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5.0 out of 5 stars Excellent to supplement lecture April 19, 2013
By Jacinda
Format:Kindle Edition|Amazon Verified Purchase
I purchased this book to help clarify some concepts I am learning in a graduate level course. Excellent job explaining these in another way to help cement the learning. I would highly recommend. Only downside is the publisher's website says we should be able to copy and paste passages from the kindle and that does not work.
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G. David Garson: Biographical Sketch

G. David Garson is full professor of public administration at North Carolina State University, where he teaches courses on advanced research methodology, geographic information systems, information technology, and American government. In 1995 he was recipient of the Donald Campbell Award from the Policy Studies Organization, American Political Science Association, for outstanding contributions to policy research methodology and in 1997 of the Aaron Wildavsky Book Award from the same organization. In 1999 he won the Okidata Instructional Web Award from the Computers and Multimedia Section of the American Political Science Association, in 2002 received an NCSU Award for Innovative Excellence in Teaching and Learning with Technology, and in 2003 received an award "For Outstanding Teaching in Political Science" from the American Political Science Association and the National Political Science Honor Society, Pi Sigma Alpha. In 2008 the NCSU Public Administration Program was named in the top 10 PA schools in the nation in information systems management. Prof. Garson is editor of and contributor to Hierarchical Linear Modeling: Guide and Applications (2012), Handbook of Public Information Systems, Third Edition. (2010); Handbook of Research on Public Information Technology (2008), Patriotic Information Systems: Privacy, Access, and Security Issues of Bush Information Policy (2008), Modern Public Information Technology Systems (2007), and author of Public Information Technology and E-Governance: Managing the Virtual State (2006), editor of Public Information Systems: Policy and Management Issues (2003), coeditor of Digital Government: Principles and Practices (2003), coauthor of Crime Mapping (2003), author of Guide to Writing Quantitative Papers, Theses, and Dissertations (Dekker, 2001), editor of Social Dimensions of Information Technology (2000), Information Technology and Computer Applications in Public Administration: Issues and Trends (1999) and is author of Neural Network Analysis for Social Scientists (1998), Computer Technology and Social Issues (1995), Geographic Databases and Analytic Mapping (1992), and is author, coauthor, editor, or coeditor of 18 other books and author or coauthor of over 50 articles. He has also created award-winning American Government computer simulations, CD-ROMs, and for the last 31 years he has also served as editor of the Social Science Computer Review and is on the editorial board of four additional journals. Professor Garson received his undergraduate degree in political science from Princeton University (1965) and his doctoral degree in government from Harvard University (1969).

Professor G. David Garson
North Carolina State University Box 8102
Raleigh, NC 27695-8102

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