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Garson, G. D. (2014). Multiple Regression. Asheboro, NC: Statistical Associates Publishers.

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Table of Contents
ISBN: 978-1-62638-031-8
@c 2014 by G. David Garson and Statistical Associates Publishers. worldwide rights reserved in all languages and on all media. Permission is not granted to copy, distribute, or post e-books or passwords.


An illustrated tutorial and introduction to multiple linear regression analysis using SPSS, SAS, or Stata. Suitable for introductory graduate-level study.

The 2014 edition is a major update to the 2012 edition. Among the new features are these:

The full content is now available from Statistical Associates Publishers. Click here.

Below is the unformatted table of contents.

Overview	13
Data examples in this volume	16
Key Terms and Concepts	17
OLS estimation	17
The regression equation	18
Dependent variable	20
Independent variables	21
Dummy variables	21
Interaction effects	22
Interactions	22
Centering	23
Significance of interaction effects	23
Interaction terms with categorical dummies	24
Plotting interactions through simple slope analysis	24
Separate regressions	27
Predicted values	28
SAS	28
Stata	29
Adjusted predicted values	30
Residuals	31
Centering	31
OLS regression in SPSS	32
Example	32
SPSS input	32
SPSS Output	33
The regression coefficient, b	33
Interpreting b for dummy variables	34
Confidence limits on b	35
Beta weights	35
Zero-order, partial, and part correlations	36
R2 and the "Model Summary" table	39
The Anova table	40
Tolerance and VIF collinearity statistics	40
SPSS plots	41
SPSS "Plots" dialog	41
Plot of standardized residuals against standardized predicted values	43
Histogram of standardized residuals	44
Normal probability (P-P) plot	45
OLS regression in SAS	46
Example	46
SAS input	47
SAS output	48
The regression coefficient, b	48
Interpreting b for dummy variables	49
Confidence limits on b	49
Beta weights	50
Zero order, partial, and part correlation	52
R-Squared and the Anova table	53
Tolerance and VIF collinearity statistics	54
SAS Plots	55
SAS plotting options	55
Plot of residuals against predicted values	57
Histogram and kernel density plot of standardized residuals	58
Normal probability (P-P) plot	59
Normal quantile-quantile (Q-Q) plot	60
Other SAS plots	61
OLS regression in Stata	64
Example	64
Stata input	65
Stata output	66
The regression coefficient, b	66
Interpreting b coefficients	67
Confidence limits on b	68
Beta weights	68
R-Squared and the Anova table	68
Zero order, partial, and part correlation	69
Tolerance and VIF collinearity statistics	69
Other Stata postestimation output	70
Stata Plots	71
Stata plotting options	71
Plot of standardized residuals against standardized predicted values	71
Histogram of standardized residuals	73
Normal probability (P-P) plot	74
Margin plots	75
Robust regression	75
Overview	75
When to use robust regression	76
Robust regression in SPSS	76
Overview	76
SPSS input	77
SPSS output	77
Robust regression in SAS	78
SAS input	78
SAS output	80
Robust regression in Stata	81
Stata input	81
Stata output	81
Hierarchical multiple regression	82
Overview	82
Examples	83
Difference in differences regression	83
Overview	83
The parallel trend assumption	84
Example data	85
Data setup	86
The model	86
Difference modeling in SPSS	89
SPSS input	89
Should the dependent variable be linear or logarithmic?	90
SPSS output	92
Difference modeling in SAS	94
SAS input	94
Should the dependent variable be linear or logarithmic?	95
SAS output	96
Difference modeling in Stata	98
Stata input	98
Should the dependent variable be linear or logarithmic?	98
Stata output	99
Panel data regression	101
Overview	101
Types of panel data regression	101
Software for panel data regression	103
Stepwise Multiple Regression	103
Overview	103
Forward, backward, and stepwise regression	103
Warning	104
Other problems of stepwise regression	105
Dummy variables in stepwise regression	105
Example	106
Stepwise regression in SPSS	106
Overview	106
SPSS input	106
SPSS Output	107
Stepwise regression in SAS	108
Overview	108
Example	109
SAS input	109
SAS output	110
Stepwise regression in Stata	111
Overview	111
Example	113
Stata input	113
Stata output	113
Model selection regression in SPSS	114
Overview	114
Example	116
The "Fields" tab	116
The "Build Options" tab	118
The "Model Options tab	123
Model Viewer	124
Default output	124
Model Viewer interface	125
Model Viewer: Automatic Data Preparation Table	127
Model Viewer: Model Building Summary window	128
Model Viewer: Coefficients window	129
Coefficient importance	132
Model Viewer: Effects window	133
Model Viewer: Predicted by Observed window	136
Model Viewer: Estimated Means window	137
Model Viewer: Residuals window	139
Model Viewer: Outliers window	141
Example 2: A boosted ensemble model	142
Model Viewer: Model Summary window	142
Model Viewer: Predictor Frequency window	142
Model Viewer: Saving and printing output	143
Model selection regression in SAS	146
Overview	146
Selection criteria	146
Example	147
SAS input	147
SAS output	148
Summary	152
Overview	152
SAS input	152
SAS output	153
Quantile Regression	158
Overview	158
Introduction	158
Pseudo-R2	159
Standard errors and coefficient significance	160
Interpreting quantile regression coefficients	161
Conditional vs. unconditional quantile regression	162
Generalized quantile regression (GQR and IVGQR)	164
Quantile Regression for Panel Data (QRPD)	166
Example	167
Quantile regression in SPSS	168
Overview	168
Heteroscedasticity test	170
SPSS input	171
SPSS output	174
Quantile regression in SAS	178
Overview	178
Heteroscedasticity test	178
SAS input	179
SAS output	180
Model selection quantile regression in SAS	186
Overview	186
Example	186
SAS input	187
SAS output	188
Quantile regression in Stata	193
Overview	193
Heteroscedasticity test	193
Stata input	194
Stata output	195
More about significance tests in regression models	199
Overview	199
Complex samples	200
F test	201
Overall test of the model and R2	201
Small samples	202
The partial F test	202
t-tests	203
One- vs. two-tailed t tests	204
t-tests for dummy variables	205
Confidence limits and standard errors	205
Confidence intervals and prediction intervals	205
The confidence interval of the regression coefficient	206
The confidence interval of y, the dependent variable	206
The prediction interval of y, the dependent variable	209
Standard error of estimate (SEE) / root mean square error (MSE)	210
Standard error and mean standard error of predicted values [SE(Pred) and MSEP]	211
More about effect size measures in multiple regression	215
Beta weights	215
Overview	215
Using beta weights in model comparisons	216
Significance of beta	217
Unique v. joint effects	217
Standardization and comparability of variables	217
Beta weights over 1.0	218
Labeling: b and beta	218
Correlation	218
Zero-order correlation, r	218
Semipartial (part) correlation	220
Partial correlation squared	220
R-squared	221
Overview	221
Warning regarding R-square differences between samples	222
Adding variables	222
Adjusted R-square	222
R-squared difference tests	224
Level-importance	232
The intercept	233
Residual analysis and diagnostics	234
Outliers, influence, leverage, and distance	234
Overview	234
Outliers and residuals	235
Leverage and distance	235
Influence	235
Example	236
Types of residuals and plots	236
Unstandardized residuals	236
Standardized residuals	236
Standardized deleted residuals	237
Studentized residuals	237
Studentized deleted residuals	238
Which type of residual to use?	238
Types of residual plots	238
Residual plots	238
Partial regression plots	239
Partial residual plots	239
Error histograms	240
Normal probability-probability (P-P) plots	240
Normal quantile-quantile (Q-Q) plots	240
Coefficients flagging unusual observations	244
Different outlier status definitions	244
Leverage values	244
Cook's distance	245
Mahalanobis distance	246
Standardized DFFITS	247
Standardized DFBETA	249
Covariance ratio (COVRATIO)	250
What to do about outliers	250
Residual analysis in SPSS	252
Obtaining residuals-related statistics	252
Saving residuals to file	253
Listing cases with the largest residuals	256
Checking for serial independence	257
Checking for homoscedastic error	257
Checking for nonlinearity	262
Checking for normally distributed error	265
Checking for outliers	271
Residual analysis in SAS	281
Obtaining residuals-related statistics	281
Saving residuals to file	284
Scatterplots of bivariate relationships	286
Listing cases with the largest residuals	287
Checking for serial independence	288
Checking for homoscedastic error	289
Checking for nonlinearity	289
Checking for normally distributed error	291
Checking for outliers	295
Other ODS plot options	304
Residual analysis in Stata	307
Obtaining residuals-related statistics	307
Saving residuals to file	307
Listing cases with the largest residuals	308
Checking for serial independence	308
Checking for homoscedastic error	309
Checking for nonlinearity	312
Checking for normally distributed error	313
Checking for outliers	318
Additional plotting options in Stata	327
Multicollinearity	327
Types of multicollinearity	328
The correlation matrix	328
Tolerance	328
VIF (variance-inflation factor)	329
Condition index values and variance proportions	330
Checking multicollinearity in SPSS	331
VIF and tolerance	331
Condition index and variance proportions	332
Checking multicollinearity in SAS	332
SAS syntax	332
VIF and tolerance	332
Condition index and variance proportions	333
Checking multicollinearity in Stata	333
VIF and tolerance	333
Condition index and variance proportions	334
Assumptions	335
Proper specification of the model	335
Spuriousness	336
Suppression	336
Ramsey's RESET test for misspecification	337
Proper specification of the research question	340
Appropriate modeling of control variables	340
Population error is assumed to be uncorrelated with each of the independent variables	341
Non-recursivity	341
No overfitting	342
Absence of perfect multicollinearity	342
Absence of high partial multicollinearity	343
Linearity	345
Nonlinear transformations	345
Nonlinear link functions	345
Data level	346
Multivariate normality	347
Normally distributed residuals (error)	348
Homoscedasticity	348
Robust standard errors	349
Robust regression	350
Outliers	350
Reliability	351
Additivity	351
Independent observations (absence of autocorrelation)	352
Overview	352
Graphical test of serial independence	353
The Durbin-Watson coefficient	357
Mean population error of zero	362
Random sampling	362
Validity	363
Other data requirements	363
Frequently Asked Questions	364
How do I report regression results?	364
What is the logic behind the calculation of regression coefficients in multiple regression?	367
How large a sample size do I need to do multiple regression?	367
Can R-squared be interpreted as the percent of the cases explained?	368
When may ordinal data be used in regression?	368
When testing for interactions, is there a strategy alternative to adding multiplicative interaction terms to the equation and testing for R2 increments?	370
How do margin plots reveal interaction effects?	371
The regress command	371
The margins command	372
The marginsplot command	373
How do I code dummy variables in regression?	375
What is "attenuation" in the context of regression?	379
Is multicollinearity only relevant if there are significant findings?	379
What can be done to handle multicollinearity?	380
What can be done to handle autocorrelation?	381
How does stepwise multiple regression relate to multicollinearity?	382
What are forward inclusion and backward elimination in stepwise regression?	382
Should I keep dropping non-significant independent variables one at a time until only significant ones remain in my model?	382
What are different types of sums of squares used in F tests?	383
Can regression be used in place of Anova for analysis of categorical independents affecting an interval dependent?	385
Does regression analysis require uncorrelated independent variables?	385
How can you test the significance of the difference between two R-squareds?	385
How do I compare b coefficients after I compute a model with the same variables for two subgroups of my sample?	386
How do I compare regression results obtained for one group of subjects to results obtained in another group, assuming the same variables were used in each regression model?	386
What do I do if I have censored, truncated, or sample-selected data?	387
What do I do if I am measuring the same independent variable at both the individual and group level?	387
What is a "relative effects" regression model?	388
How do I test to see what effect a quadratic or other nonlinear term makes in my regression model?	389
What is "smoothing" in regression and how does it relate to dealing with nonlinearities in OLS regression?	389
What is nonparametric regression for nonlinear relationships?	391
What is Poisson regression?	394
SPSS questions	394
What is the command syntax for linear regression in SPSS?	394
How do I standardize variables in SPSS?	396
How do I create interaction variables in SPSS?	396
All I want is a simple scatterplot with a regression line. Why won't SPSS give it to me?	397
What is categorical regression in SPSS?	398
Acknowledgments	399
Bibliography	400
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