Practice

1
(No Transcript)
2
Practice

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

3
(No Transcript)
4
How many risk behaviors would a child likely
engage in if they are 12 years old and were
monitored 1?
5
How many risk behaviors would a child likely
engage in if they are 12 years old and were
monitored 1? 1.72 behaviors
6
How many risk behaviors would a child likely
engage in if they are 12 years old and were
monitored 4?
7
How many risk behaviors would a child likely
engage in if they are 12 years old and were
monitored 4? .51 behaviors
8
What has a bigger effect on risk behaviors
age or monitoring?
9
Did the entire model significantly predict risk
behaviors?
10
Significance testing for Multiple R
p number of predictors N total number of
observations
11
Significance testing for Multiple R
p number of predictors N total number of
observations
12
(No Transcript)
13
What is the correlation between age and risk
controlling for monitoring? What is the
correlation between monitoring and risk
controlling for age?
14
(No Transcript)
15
(No Transcript)
16
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

17
(No Transcript)
18
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

19
Testing for Significance

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

20
Remember

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

21
Remember

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

22
Significance Testing

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

23
Significance Testing
sr semipartial correlation being tested N
total number of people p total number of
predictors R Multiple R containing the sr
24
Multiple R
25
Significance Testing
N 15 p 2 R2 .53 sr .17
26
Significance Testing

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

27
t distribution
tcrit -2.179
tcrit 2.179
0
28
t distribution
tcrit -2.179
tcrit 2.179
0
.85
29

• 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

30
Practice

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

31
Significance Testing
N 15 p 2 R2 .53 sr .43
32
Practice

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

33
Significance Testing

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

34
t distribution
tcrit -2.179
tcrit 2.179
0
35
t distribution
tcrit -2.179
tcrit 2.179
0
2.172
36

• 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

37
(No Transcript)
38
Remember

• Calculate t-observed

b Slope Sb Standard error of slope
39
(No Transcript)
40
(No Transcript)
41
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?

42
(No Transcript)
43
Common Applications of Regression
44
Common Applications of Regression

• Mediating Models

Teaching Evals
Candy
45
Common Applications of Regression

• Mediating Models

Happy
Teaching Evals
Candy
46
Mediating Relationships

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

47
Mediating Relationships
Mediator
b
a
c
DV
IV
48
Mediating Relationships
Mediator
a
IV
1. There is a relationship between the IV and the
Mediator
49
Mediating Relationships
Mediator
b
DV
2. There is a relationship between the Mediator
and the DV
50
Mediating Relationships
c
DV
IV
3. There is a relationship between the IV and DV
51
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
52
Example

• Mediating Models

Happy
Teaching Evals
Candy
53
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
54
(No Transcript)
55
Mediating Relationships
Happy
.23
Candy
1. There is a relationship between the IV and the
Mediator
56
Mediating Relationships
Happy
.83
Eval
2. There is a relationship between the Mediator
and the DV
57
Mediating Relationships
.40
Eval
Candy
3. There is a relationship between the IV and DV
58
(No Transcript)
59
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
60
Note

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

61
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

62
(No Transcript)
63
Mediating Relationships
Talk
.34
Extraversion
1. There is a relationship between the IV and the
Mediator
64
Mediating Relationships
Talk
.57
Like
2. There is a relationship between the Mediator
and the DV
65
Mediating Relationships
.26
Like
Extraversion
3. There is a relationship between the IV and DV
66
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
67
(No Transcript)
68
(No Transcript)
69
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

70
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)

71
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

72
(No Transcript)
73
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

74
(No Transcript)
75
(No Transcript)
76
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)

77
(No Transcript)
78
Graphing a Moderating Variable
79
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.
80
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)
81
puberty Open op Pred Y
0 -1.14 0
0 0 0
0 1.14 0
82
puberty Open op Pred Y
0 -1.14 0 2.87
0 0 0 3.15
0 1.14 0 3.43
83
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
84
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
85
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
86
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
87
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
88
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
89
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
90
More Dev. Average Dev. Less Dev.
-1.14 0 1.14