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
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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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