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Date:         Fri, 18 Jan 2008 14:36:36 -0600
Reply-To:     Justin Meyer <justin.meyer@rowlandreading.org>
Sender:       "SPSSX(r) Discussion" <SPSSX-L@LISTSERV.UGA.EDU>
From:         Justin Meyer <justin.meyer@rowlandreading.org>
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 <http://www.rowlandreading.org/>

____________________________________

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