```Date: Fri, 18 Jan 2008 14:36:36 -0600 Reply-To: Justin Meyer Sender: "SPSSX(r) Discussion" From: Justin Meyer Subject: Dummy Coding and Interpreting Regression Analysis Content-Type: text/plain; charset="us-ascii" SPSS Listers: I am working to determine if a subjective rating of schools' implementation is a predictor of posttest score for students in those schools. In previous analyses, the significant predictors of posttest score were pretest score (scaled score from about 300 to 600), gender of student (male or female) and economic status of student (Free lunch or not). For the subjective rating of schools' implementation, schools are rated as tier 1, 2, or 3, with 1 being the best implementation and 3 being the worst. I am using a regression analysis, entering all of the variables at the same time. Because the tier status consists of three possible responses, I dummy coded it into two variables. The first variable is 1 for "Tier 2", 0 for "not Tier 2". The second variable is 1 for "Tier 3", and 0 for "not Tier 3". Is this the correct way to code this variable for a regression analysis? Also, I found a b (unstandardized coefficient) of -10.269 for Tier 2 and 21.171 for Tier 3. Does this mean that, when all other variables are equal, students in Tier 2 score an average of 10 points less on the posttest and students in Tier 3 score an average of 21 points more on the posttest when compared to Tier 1? Or are the unstandardized coefficients comparing Tier 2 with both Tiers 1 and 3 and Tier 3 with both Tiers 1 and 2, respectively? This seems like a simple question, but I can't find much information about how dummy coding works. Thank you for any help you can provide. Let me know if I need to explain more. The output from the regression, except for charts, is pasted below: Descriptive Statistics Mean Std. Deviation N sscaled_score1 503.15 51.110 1970 scaled_score1 426.24 44.629 1970 gender_Recoded .51 .500 1970 economic_status_recodedRecoded .2766 .44746 1970 School is Tier 2 .25 .434 1970 School is Tier 3 .02 .144 1970 Correlations sscaled_score1 scaled_score1 gender_Recoded economic_status_recodedRecoded School is Tier 2 School is Tier 3 Pearson Correlation sscaled_score1 1.000 .710 .103 -.264 -.117 .075 scaled_score1 .710 1.000 .090 -.239 -.052 .027 gender_Recoded .103 .090 1.000 -.012 .009 .006 economic_status_recodedRecoded -.264 -.239 -.012 1.000 -.088 .097 School is Tier 2 -.117 -.052 .009 -.088 1.000 -.086 School is Tier 3 .075 .027 .006 .097 -.086 1.000 Sig. (1-tailed) sscaled_score1 . .000 .000 .000 .000 .000 scaled_score1 .000 . .000 .000 .011 .112 gender_Recoded .000 .000 . .298 .340 .403 economic_status_recodedRecoded .000 .000 .298 . .000 .000 School is Tier 2 .000 .011 .340 .000 . .000 School is Tier 3 .000 .112 .403 .000 .000 . N sscaled_score1 1970 1970 1970 1970 1970 1970 scaled_score1 1970 1970 1970 1970 1970 1970 gender_Recoded 1970 1970 1970 1970 1970 1970 economic_status_recodedRecoded 1970 1970 1970 1970 1970 1970 School is Tier 2 1970 1970 1970 1970 1970 1970 School is Tier 3 1970 1970 1970 1970 1970 1970 Variables Entered/Removed(b) Model Variables Entered Variables Removed Method 1 School is Tier 3, gender_Recoded, School is Tier 2, scaled_score1, economic_status_recodedRecoded(a) . Enter a All requested variables entered. b Dependent Variable: sscaled_score1 Model Summary(b) Model R R Square Adjusted R Square Std. Error of the Estimate 1 .726(a) .526 .525 35.220 a Predictors: (Constant), School is Tier 3, gender_Recoded, School is Tier 2, scaled_score1, economic_status_recodedRecoded b Dependent Variable: sscaled_score1 ANOVA(b) Model Sum of Squares df Mean Square F Sig. 1 Regression 2707279.702 5 541455.940 436.512 .000(a) Residual 2436172.778 1964 1240.414 Total 5143452.479 1969 a Predictors: (Constant), School is Tier 3, gender_Recoded, School is Tier 2, scaled_score1, economic_status_recodedRecoded b Dependent Variable: sscaled_score1 Coefficients(a) Model Unstandardized Coefficients Standardized Coefficients t Sig. Correlations Collinearity Statistics B Std. Error Beta Zero-orderPartial Part Tolerance VIF B Std. Error 1 (Constant) 178.839 8.063 22.181 .000 scaled_score1 .769 .018 .672 41.675 .000 .710 .685 .647 .928 1.078 gender_Recoded 4.282 1.594 .042 2.687 .007 .103 .061 .042 .992 1.009 economic_status_recodedRecoded -13.272 1.846 -.116 -7.191 .000 -.264 -.160 -.112 .924 1.083 School is Tier 2 -10.269 1.845 -.087 -5.567 .000 -.117 -.125 -.086 .981 1.019 School is Tier 3 21.171 5.542 .060 3.820 .000 .075 .086 .059 .982 1.018 a Dependent Variable: sscaled_score1 Coefficient Correlations(a) Model School is Tier 3 gender_Recoded School is Tier 2 scaled_score1 economic_status_recodedRecoded 1 Correlations School is Tier 3 1.000 -.003 .074 -.046 -.099 gender_Recoded -.003 1.000 -.015 -.090 -.011 School is Tier 2 .074 -.015 1.000 .073 .095 scaled_score1 -.046 -.090 .073 1.000 .248 economic_status_recodedRecoded -.099 -.011 .095 .248 1.000 Covariances School is Tier 3 30.719 -.028 .760 -.005 -1.014 gender_Recoded -.028 2.540 -.045 -.003 -.032 School is Tier 2 .760 -.045 3.402 .002 .323 scaled_score1 -.005 -.003 .002 .000 .008 economic_status_recodedRecoded -1.014 -.032 .323 .008 3.407 a Dependent Variable: sscaled_score1 Collinearity Diagnostics(a) Model Dimension Eigenvalue Condition Index Variance Proportions (Constant)scaled_score1 gender_Recoded economic_status_recodedRecoded School is Tier 2 School is Tier 3 (Constant) scaled_score1 1 1 3.277 1.000 .00 .00 .03 .02 .02 .00 2 1.025 1.788 .00 .00 .00 .04 .10 .74 3 .746 2.096 .00 .00 .00 .38 .38 .25 4 .604 2.328 .00 .00 .23 .38 .39 .00 5 .342 3.095 .01 .01 .73 .10 .09 .00 6 .005 25.692 .99 .99 .00 .08 .01 .00 a Dependent Variable: sscaled_score1 Residuals Statistics(a) Minimum Maximum Mean Std. Deviation N Predicted Value 385.35 631.69 503.15 37.080 1970 Std. Predicted Value -3.177 3.467 .000 1.000 1970 Standard Error of Predicted Value 1.324 6.064 1.826 .666 1970 Adjusted Predicted Value 385.36 632.21 503.15 37.087 1970 Residual -119.496 155.510 .000 35.175 1970 Std. Residual -3.393 4.415 .000 .999 1970 Stud. Residual -3.405 4.421 .000 1.000 1970 Deleted Residual -120.366 155.897 -.001 35.286 1970 Stud. Deleted Residual -3.414 4.442 .000 1.001 1970 Mahal. Distance 1.785 57.368 4.997 6.982 1970 Cook's Distance .000 .026 .001 .001 1970 Centered Leverage Value .001 .029 .003 .004 1970 a Dependent Variable: sscaled_score1 ____________________________________ Justin Meyer Researcher Rowland Reading Foundation 1 South Pinckney Street, Suite 324 Madison, WI 53703 phone: 866-370-7323 fax: 608-204-3846 www.rowlandreading.org ____________________________________ ====================To manage your subscription to SPSSX-L, send a message to LISTSERV@LISTSERV.UGA.EDU (not to SPSSX-L), with no body text except the command. To leave the list, send the command SIGNOFF SPSSX-L For a list of commands to manage subscriptions, send the command INFO REFCARD ```

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