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Common Applications of Regression
Common Applications of Regression
• Mediating Models
Candy Teaching Evals
Happy
Mediating Relationships
IVDV
Mediator
ab
c
Mediating Relationships
IV
Mediator
a
1. There is a relationship between the IV and the Mediator
Mediating Relationships
DV
Mediator
b
2. There is a relationship between the Mediator and the DV
Mediating Relationships
IVDV
c
3. There is a relationship between the IV and DV
Mediating Relationships
IVDV
Mediator
ab
c
4. When both the IV and mediator are used to predict the DV the importance of path c is greatly reduced
Common Applications of Regression
• Moderating Models
• Does the relationship between the IV and DV change as a function of the level of a third variable
• Interaction
Example
• Girls risk behavior– Cigarettes, alcohol, pot, kissing
• Openness to experience
• Pubertal Development
• How might pubertal development moderate the relationship between openness and participation in risk behaviors?– Note: pubertal development is the variable you think moderates
the relationship (mathematically this is irrelevant)
Example
• Data were collected from 20 girls
• Mother’s rating of openness
• Doctor’s rating of pubertal development
• One year later girls report of risk behaviors– Sum risk behavior
1.000 .143 .330
.143 1.000 .637**
.330 .637** 1.000
. .547 .156
.547 . .002
.156 .002 .
20 20 20
20 20 20
20 20 20
PUB
OPEN
RISK
PUB
OPEN
RISK
PUB
OPEN
RISK
PearsonCorrelation
Sig.(2-tailed)
N
PUB OPEN RISK
Correlations
Correlation is significant at the 0.01 level (2-tailed).**.
How do you examine an interaction?
• Multiply the two variables you think will interact with each other– Openness x puberty
• Should always center these variables BEFORE multiplying them– Reduces the relationship between them and
the resulting interaction term
1.000 .143 .330
.143 1.000 .637**
.330 .637** 1.000
. .547 .156
.547 . .002
.156 .002 .
20 20 20
20 20 20
20 20 20
PUB
OPEN
RISK
PUB
OPEN
RISK
PUB
OPEN
RISK
PearsonCorrelation
Sig.(2-tailed)
N
PUB OPEN RISK
Correlations
Correlation is significant at the 0.01 level (2-tailed).**.
1.000 .143 .330
.143 1.000 .637**
.330 .637** 1.000
. .547 .156
.547 . .002
.156 .002 .
20 20 20
20 20 20
20 20 20
CPUB
COPEN
RISK
CPUB
COPEN
RISK
CPUB
COPEN
RISK
PearsonCorrelation
Sig.(2-tailed)
N
CPUB COPEN RISK
Correlations
Correlation is significant at the 0.01 level (2-tailed).**.
1.000 .143 .000
.143 1.000 .278
.000 .278 1.000
. .547 1.000
.547 . .235
1.000 .235 .
20 20 20
20 20 20
20 20 20
CPUB
COPEN
CINTER
CPUB
COPEN
CINTER
CPUB
COPEN
CINTER
PearsonCorrelation
Sig.(2-tailed)
N
CPUB COPEN CINTER
Correlations
1.000 .143 .693**
.143 1.000 .766**
.693** .766** 1.000
. .547 .001
.547 . .000
.001 .000 .
20 20 20
20 20 20
20 20 20
PUB
OPEN
INTER
PUB
OPEN
INTER
PUB
OPEN
INTER
PearsonCorrelation
Sig.(2-tailed)
N
PUB OPEN INTER
Correlations
Correlation is significant at the 0.01 level (2-tailed).**.
How do you examine an interaction?
• Conduct a regression with:
• Centered IV1 (openness)
• Centered IV2 (puberty)
• Interaction of these (open x puberty)
• Predicting outcome (Sum Risk)
3.149 .091 34.569 .000
.161 .081 .265 1.971 .066
.246 .076 .454 3.245 .005
.257 .068 .525 3.792 .002
(Constant)
CPUB
COPEN
CINTER
Model1
B Std. Error
UnstandardizedCoefficients
Beta
Standardized
Coefficients
t Sig.
Coefficientsa
Dependent Variable: RISKa.
Graphing a Moderating Variable
)*(257.)(161.)(246.149.3ˆ cpubertycopencpubertycopenY
Graphing a Moderating Variable
Using this information it is possible to predict what a girl’s risk behavior would for different levels of openness and puberty.
)*(257.)(161.)(246.149.3ˆ cpubertycopencpubertycopenY
Graphing a Moderating Variable
)*(257.)(161.)(246.149.3ˆ cpubertycopencpubertycopenY
Using this information it is possible to predict what a girl’s risk behavior would for different levels of openness and puberty.
For example -- Imagine 3 girls who have average development (i.e., cpuberty = 0).
One girl’s openness is 1 sd below the mean (copen = -1.14)
One girl’s opennes is at the mean (copen = 0)
One girl’s openness is 1 sd above the mean (copen = 1.14)
puberty Open o*p Pred Y
0 -1.14 0
0 0 0
0 1.14 0
)*(257.)(161.)(246.149.3ˆ cpubertycopencpubertycopenY
puberty Open o*p Pred Y
0 -1.14 0 2.87
0 0 0 3.15
0 1.14 0 3.43
)*(257.)(161.)(246.149.3ˆ cpubertycopencpubertycopenY
2
3
4
5
Openness
Ris
k B
ehav
ior
-1.14 0 1.14
puberty Open o*p Pred Y
0 -1.14 0 2.87
0 0 0 3.15
0 1.14 0 3.43
puberty Open o*p Pred Y
1.28 -1.14 -1.46
1.28 0 0
1.28 1.14 1.46
0 -1.14 0 2.87
0 0 0 3.15
0 1.14 0 3.43
More
Average
When graphing out – make different “lines” for each level of the variable you conceptualized as moderating
)*(257.)(161.)(246.149.3ˆ cpubertycopencpubertycopenY
puberty Open o*p Pred Y
1.28 -1.14 -1.46 2.70
1.28 0 0 3.36
1.28 1.14 1.46 4.02
0 -1.14 0 2.87
0 0 0 3.15
0 1.14 0 3.43
More
Average
When graphing out – make different “lines” for each level of the variable you conceptualized as moderating
)*(257.)(161.)(246.149.3ˆ cpubertycopencpubertycopenY
2
3
4
5
Openness
Ris
k B
ehav
ior
-1.14 0 1.14
puberty Open o*p Pred Y
1.28 -1.14 -1.46 2.70
1.28 0 0 3.36
1.28 1.14 1.46 4.02
puberty Open o*p Pred Y
1.28 -1.14 -1.46 2.70
1.28 0 0 3.36
1.28 1.14 1.46 4.02
0 -1.14 0 2.87
0 0 0 3.15
0 1.14 0 3.43
-1.28 -1.14 1.46
-1.28 0 0
-1.28 1.14 -1.46
More
Average
Less
When graphing out – make different “lines” for each level of the variable you conceptualized as moderating
)*(257.)(161.)(246.149.3ˆ cpubertycopencpubertycopenY
puberty Open o*p Pred Y
1.28 -1.14 -1.46 2.70
1.28 0 0 3.36
1.28 1.14 1.46 4.02
0 -1.14 0 2.87
0 0 0 3.15
0 1.14 0 3.43
-1.28 -1.14 1.46 3.09
-1.28 0 0 2.94
-1.28 1.14 -1.46 2.84
More
Average
Less
When graphing out – make different “lines” for each level of the variable you conceptualized as moderating
)*(257.)(161.)(246.149.3ˆ cpubertycopencpubertycopenY
2
3
4
5
Openness
Ris
k B
ehav
ior
-1.14 0 1.14
puberty Open o*p Pred Y
-1.28 -1.14 1.46 3.09
-1.28 0 0 2.94
-1.28 1.14 -1.46 2.84
2
3
4
5
Openness
Ris
k B
ehav
ior
-1.14 0 1.14
More Dev.
Average Dev.
Less Dev.
Practice
• Based on past research you know that martial happiness is related unhealthy dieting habits in women.
• However, you think that women’s esteem might moderate this relationship– Specifically, you think a woman with high self esteem
will not be affected as greatly by a poor marriage as a woman with low self-esteem
Practice
• Date were collected from 172 women
• Martial Quality (M = 0; SD = 1)• Esteem (M = 0; SD = 1)• Unhealthy Dieting (Range 0 - 19)
• Determine if esteem moderated the relationship between marital quality and unhealthy dieting
2.528 .183 13.787 .000
-.681 .199 -.266 -3.431 .001
-.303 .187 -.118 -1.623 .107
.389 .151 .193 2.573 .011
(Constant)
ZESTEEM Zscore(ESTEEM)
ZMARQUAL Zscore(MARQUAL)
INTERAC
Model1
B Std. Error
UnstandardizedCoefficients
Beta
Standardized
Coefficients
t Sig.
Coefficientsa
Dependent Variable: UNDIETa.
)*(389.)(303.)(681.53.2ˆ esteemmarmarestY
2.528 .183 13.787 .000
-.681 .199 -.266 -3.431 .001
-.303 .187 -.118 -1.623 .107
.389 .151 .193 2.573 .011
(Constant)
ZESTEEM Zscore(ESTEEM)
ZMARQUAL Zscore(MARQUAL)
INTERAC
Model1
B Std. Error
UnstandardizedCoefficients
Beta
Standardized
Coefficients
t Sig.
Coefficientsa
Dependent Variable: UNDIETa.
Est Mar E*M Pred Y
-1 -1 1 3.90
-1 0 0 3.21
-1 1 -1 2.51
0 -1 0 2.83
0 0 0 2.53
0 1 0 2.23
1 -1 -1 1.76
1 0 0 1.85
1 1 1 1.93
Low
Mod
High
When graphing out – make different “lines” for each level of the variable you conceptualized as moderating
)*(389.)(303.)(681.53.2ˆ esteemmarmarestY
1
1.5
2
2.5
3
3.5
4
Marital Quality
Un
hea
lth
y D
ieti
ng
-1 0 1
High SE
Average SE
Low SE
Handout
• DV = Risk Behavior (0 – 4)
• IV = Child’s perception of monitoring
• IV = Objective measure of monitoring
Handout Practice
• 1) Draw a causal model using the standardized regression coefficients.
• 2) Determine if the overall model significantly predicts risk behavior.
• 3) Compute the semipartial correlation for each IV
• 4) Determine if the unstandardized regression weights are significant.
• 5) Discuss in a few sentences what is the overall “story” being told by these data