Practice

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Practice

• N 130
• Risk behaviors (DV Range 0 4)
• Age (IV M 10.8)
• Monitoring (IV Range 1 4)

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How many risk behaviors would a child likely
engage in if they are 12 years old and were
monitored 1?
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How many risk behaviors would a child likely
engage in if they are 12 years old and were
monitored 1? 1.72 behaviors
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How many risk behaviors would a child likely
engage in if they are 12 years old and were
monitored 4?
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How many risk behaviors would a child likely
engage in if they are 12 years old and were
monitored 4? .51 behaviors
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What has a bigger effect on risk behaviors
age or monitoring?
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Did the entire model significantly predict risk
behaviors?
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Significance testing for Multiple R
p number of predictors N total number of
observations
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Significance testing for Multiple R
p number of predictors N total number of
observations
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What is the correlation between age and risk
controlling for monitoring? What is the
correlation between monitoring and risk
controlling for age?
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Quick Review

• Predict using 2 or more IVs
• Test the fit of this overall model
• Multiple R Significance test
• Standardize the model
• Betas
• Compute correlations controlling for other
  variables
• Semipartical correlations

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Testing for Significance

• Once an equation is created (standardized or
  unstandardized) typically test for significance.
• Two levels
• 1) Level of each regression coefficient
• 2) Level of the entire model

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Testing for Significance

• Note Significance tests are the same for
• Unstandarized Regression Coefficients
• Standardized Regression Coefficients
• Semipartial Correlations

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Remember

• Y Salary
• X1 Years since Ph.D. X2 Publications
• rs(P.Y) .17

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Remember

• Y Salary
• X1 Years since Ph.D. X2 Publications
• rs(P.Y) .17

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Significance Testing

• H1 sr, b, or ß is not equal to zero
• Ho sr, b, or ß is equal to zero

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Significance Testing
sr semipartial correlation being tested N
total number of people p total number of
predictors R Multiple R containing the sr
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Multiple R
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Significance Testing
N 15 p 2 R2 .53 sr .17
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Significance Testing

• t critical
• df N p 1
• df 15 2 1 12
• t critical 2.179 (two-tailed)

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t distribution
tcrit -2.179
tcrit 2.179
0
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t distribution
tcrit -2.179
tcrit 2.179
0
.85
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• If tobs falls in the critical region
• Reject H0, and accept H1
• If tobs does not fall in the critical region
• Fail to reject H0
• sr, b2, and ß2 are not significantly different
  than zero

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Practice

• Determine if 977 increase for each year in the
  equation is significantly different than zero.

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Significance Testing
N 15 p 2 R2 .53 sr .43
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Practice

• Determine if 977 increase for each year in the
  equation is significantly different than zero.

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Significance Testing

• t critical
• df N p 1
• df 15 2 1 12
• t critical 2.179 (two-tailed)

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t distribution
tcrit -2.179
tcrit 2.179
0
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t distribution
tcrit -2.179
tcrit 2.179
0
2.172
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• If tobs falls in the critical region
• Reject H0, and accept H1
• If tobs does not fall in the critical region
• Fail to reject H0
• sr, b2, and ß2 are not significantly different
  than zero

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Remember

• Calculate t-observed

b Slope Sb Standard error of slope
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Significance Test

• It is possible (as in this last problem) to have
  the entire model be significant but no single
  predictor be significant how is that possible?

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Common Applications of Regression
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Common Applications of Regression

• Mediating Models

Teaching Evals
Candy
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Common Applications of Regression

• Mediating Models

Happy
Teaching Evals
Candy
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Mediating Relationships

• How do you know when you have a mediating
  relationship?
• Baron Kenny (1986)

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Mediating Relationships
Mediator
b
a
c
DV
IV
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Mediating Relationships
Mediator
a
IV
1. There is a relationship between the IV and the
Mediator
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Mediating Relationships
Mediator
b
DV
2. There is a relationship between the Mediator
and the DV
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Mediating Relationships
c
DV
IV
3. There is a relationship between the IV and DV
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Mediating Relationships
Mediator
b
a
c
DV
IV
3. When both the IV and mediator are used to
predict the DV the importance of path c is
greatly reduced
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Example

• Mediating Models

Happy
Teaching Evals
Candy
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Candy Happy Eval 1.00 2.00 1.00 1.00 3.00 1.00 1.0
0 4.00 2.00 1.00 5.00 2.00 1.00 2.00 2.00 2.00 4.0
0 3.00 2.00 2.00 3.00 2.00 4.00 3.00 2.00 7.00 4.0
0 1.00 4.00 2.00 1.00 6.00 3.00 1.00 8.00 4.00 1.0
0 6.00 4.00 2.00 2.00 1.00 2.00 5.00 2.00 2.00 8.0
0 4.00 2.00 6.00 4.00 2.00 8.00 4.00 1.00 1.00 1.0
0
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Mediating Relationships
Happy
.23
Candy
1. There is a relationship between the IV and the
Mediator
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Mediating Relationships
Happy
.83
Eval
2. There is a relationship between the Mediator
and the DV
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Mediating Relationships
.40
Eval
Candy
3. There is a relationship between the IV and DV
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Mediating Relationships
Happy
.78
.28
.22
Eval
Candy
3. When both the IV and mediator are used to
predict the DV the importance of path c is
greatly reduced
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Note

• Does not prove cause
• It is an assumption of the model!
• Can think of this also in terms of the
  semipartial correlation

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Practice

• You know from past research that extraverts tend
  to be well liked by others.
• You hypothesize that this is because they talk
  more often.
• You collect data from 100 subjects
• Extraversion
• Talkativeness
• How much friends like them
• Determine if your hypothesis is correct

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Mediating Relationships
Talk
.34
Extraversion
1. There is a relationship between the IV and the
Mediator
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Mediating Relationships
Talk
.57
Like
2. There is a relationship between the Mediator
and the DV
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Mediating Relationships
.26
Like
Extraversion
3. There is a relationship between the IV and DV
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Mediating Relationships
Talk
.54
.34
.07
Like
Extraversion
4. When both the IV and mediator are used to
predict the DV the importance of path c is
greatly reduced
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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

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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)

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Example

• Data were collected from 20 girls
• Mothers rating of openness
• Doctors rating of pubertal development
• One year later girls report of risk behaviors
• Sum risk behavior

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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

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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)

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Graphing a Moderating Variable
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Graphing a Moderating Variable
Using this information it is possible to predict
what a girls risk behavior would for different
levels of openness and puberty.
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Graphing a Moderating Variable
Using this information it is possible to predict
what a girls risk behavior would for different
levels of openness and puberty.
For example -- Imagine 3 girls who have average
development (i.e., cpuberty 0). One girls
openness is 1 sd below the mean (copen
-1.14) One girls opennes is at the mean (copen
0) One girls openness is 1 sd above the mean
(copen 1.14)
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puberty Open op Pred Y
0 -1.14 0
0 0 0
0 1.14 0
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puberty Open op Pred Y
0 -1.14 0 2.87
0 0 0 3.15
0 1.14 0 3.43
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puberty Open op Pred Y
0 -1.14 0 2.87
0 0 0 3.15
0 1.14 0 3.43
-1.14 0 1.14
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puberty Open op 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
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puberty Open op 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
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puberty Open op Pred Y
1.28 -1.14 -1.46 2.70
1.28 0 0 3.36
1.28 1.14 1.46 4.02
-1.14 0 1.14
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puberty Open op 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
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puberty Open op 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
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puberty Open op Pred Y
-1.28 -1.14 1.46 3.09
-1.28 0 0 2.94
-1.28 1.14 -1.46 2.84
-1.14 0 1.14
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More Dev. Average Dev. Less Dev.
-1.14 0 1.14
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Practice

• Based on past research you know that martial
  happiness is related unhealthy dieting habits in
  women.
• However, you think that womens 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

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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

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Est Mar EM 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
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Low SE
Average SE
High SE
-1 0 1