2. Practice N = 130 Risk behaviors (DV; Range 0 – 4) Age (IV; M = 10.8)
Monitoring (IV; Range 1 – 4)

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

13. What is the correlation between age and risk controlling for monitoring?
What is the correlation between monitoring and risk controlling for age?

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

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 β is not equal to zero
Ho = sr, b, or β 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 = (two-tailed)

27. t distribution
tcrit =
tcrit = 2.179

28. t distribution
tcrit =
tcrit = 2.179
.85

29. sr, b2, and β2 are not significantly different than zero
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 β2 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 = (two-tailed)

34. t distribution
tcrit =
tcrit = 2.179

35. t distribution
tcrit =
tcrit = 2.179
2.172

36. sr, b2, and β2 are not significantly different than zero
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 β2 are not significantly different than zero

38. Remember
Calculate t-observed
b = Slope
Sb = Standard error of slope

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?

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 Relationshipsc 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

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

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

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

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 Openness to experience
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 Mother’s rating of openness
Doctor’s rating of pubertal development
One year later girls report of risk behaviors
Sum risk behavior

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

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)

78. Graphing a Moderating Variable

79. 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.

80. 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.
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)

81. puberty
Open
o*p
Pred Y
-1.14
1.14

82. puberty
Open
o*p
Pred Y
-1.14
2.87
3.15
1.14
3.43

83. puberty
Open
o*p
Pred Y
-1.14
2.87
3.15
1.14
3.43

84. puberty Open o*p Pred Y 1.28 -1.14 -1.46 1.14 1.46 2.87 3.15 3.43 More
1.14
1.46
2.87
3.15
3.43
More
Average
When graphing out – make different “lines” for each level of the variable you conceptualized as moderating

85. puberty Open o*p Pred Y 1.28 -1.14 -1.46 2.70 3.36 1.14 1.46 4.02 2.87
3.36
1.14
1.46
4.02
2.87
3.15
3.43
More
Average
When graphing out – make different “lines” for each level of the variable you conceptualized as moderating

86. puberty Open o*p Pred Y 1.28 -1.14 -1.46 2.70 3.36 1.14 1.46 4.02
3.36
1.14
1.46
4.02

87. puberty Open o*p Pred Y 1.28 -1.14 -1.46 2.70 3.36 1.14 1.46 4.02 2.87
3.36
1.14
1.46
4.02
2.87
3.15
3.43
-1.28
More
Average
Less
When graphing out – make different “lines” for each level of the variable you conceptualized as moderating

88. puberty Open o*p Pred Y 1.28 -1.14 -1.46 2.70 3.36 1.14 1.46 4.02 2.87
3.36
1.14
1.46
4.02
2.87
3.15
3.43
-1.28
3.09
2.94
2.84
More
Average
Less
When graphing out – make different “lines” for each level of the variable you conceptualized as moderating

89. puberty Open o*p Pred Y -1.28 -1.14 1.46 3.09 2.94 1.14 -1.46 2.84
2.94
1.14
-1.46
2.84

90. More Dev.
Average Dev.
Less Dev.

91. 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

92. Practice Date were collected from 172 women
Martial Quality (M = 0; SD = 1)
Esteem (M = 0; SD = 1)
Unhealthy Dieting (Range )
Determine if esteem moderated the relationship between marital quality and unhealthy dieting

95. Est
Mar
E*M
Pred Y -1 1
3.90
3.21
2.51
2.83
2.53
2.23
1.76
1.85
1.93
Low
Mod
High
When graphing out – make different “lines” for each level of the variable you conceptualized as moderating

96. Low SE
Average SE
High SE