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

How many risk behaviors would a child likely engage in if they are 12 years old and were monitored “1”?

How many risk behaviors would a child likely engage in if they are 12 years old and were monitored “1”? = 1.72 behaviors

How many risk behaviors would a child likely engage in if they are 12 years old and were monitored “4”?

How many risk behaviors would a child likely engage in if they are 12 years old and were monitored “4”? .51 behaviors

What has a bigger “effect” on risk behaviors – age or monitoring?

Did the entire model significantly predict risk behaviors?

Significance testing for Multiple R p = number of predictors N = total number of observations

Significance testing for Multiple R p = number of predictors N = total number of observations

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

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

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

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

Remember Y = Salary X1 = Years since Ph.D.; X2 = Publications rs(P.Y) = .17

Remember Y = Salary X1 = Years since Ph.D.; X2 = Publications rs(P.Y) = .17

Significance Testing H1 = sr, b, or β is not equal to zero Ho = sr, b, or β is equal to zero

Significance Testing sr = semipartial correlation being tested N = total number of people p = total number of predictors R = Multiple R containing the sr

Multiple R

Significance Testing N = 15 p = 2 R2 = .53 sr = .17

Significance Testing t critical df = N – p – 1 df = 15 – 2 – 1 = 12 t critical = 2.179 (two-tailed)

t distribution tcrit = -2.179 tcrit = 2.179

t distribution tcrit = -2.179 tcrit = 2.179 .85

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

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

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

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

Significance Testing t critical df = N – p – 1 df = 15 – 2 – 1 = 12 t critical = 2.179 (two-tailed)

t distribution tcrit = -2.179 tcrit = 2.179

t distribution tcrit = -2.179 tcrit = 2.179 2.172

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

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

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?

Common Applications of Regression

Common Applications of Regression Mediating Models Teaching Evals Candy

Common Applications of Regression Mediating Models Happy Teaching Evals Candy

Mediating Relationships How do you know when you have a mediating relationship? Baron & Kenny (1986)

Mediating Relationships Mediator b a c DV IV

Mediating Relationships Mediator a IV 1. There is a relationship between the IV and the Mediator

Mediating Relationships Mediator b DV 2. There is a relationship between the Mediator and the DV

Mediating Relationships c DV IV 3. There is a relationship between the IV and DV

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

Example Mediating Models Happy Teaching Evals Candy

Candy Happy Eval 1.00 2.00 1.00 1.00 3.00 1.00 1.00 4.00 2.00 1.00 5.00 2.00 1.00 2.00 2.00 2.00 4.00 3.00 2.00 2.00 3.00 2.00 7.00 4.00 1.00 6.00 3.00 1.00 8.00 4.00 1.00 6.00 4.00 2.00 2.00 1.00 2.00 5.00 2.00 2.00 8.00 4.00 2.00 6.00 4.00 1.00 1.00 1.00

Mediating Relationships Happy .23 Candy 1. There is a relationship between the IV and the Mediator

Mediating Relationships Happy .83 Eval 2. There is a relationship between the Mediator and the DV

Mediating Relationships .40 Eval Candy 3. There is a relationship between the IV and DV

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

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

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

Mediating Relationships Talk .34 Extraversion 1. There is a relationship between the IV and the Mediator

Mediating Relationships Talk .57 Like 2. There is a relationship between the Mediator and the DV

Mediating Relationships .26 Like Extraversion 3. There is a relationship between the IV and DV

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

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 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)

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

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

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)

Graphing a Moderating Variable

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.

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)

puberty Open o*p Pred Y -1.14 1.14

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

puberty Open o*p Pred Y -1.14 2.87 3.15 1.14 3.43 -1.14 0 1.14

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

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

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 -1.14 0 1.14

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

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

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 -1.14 0 1.14

More Dev. Average Dev. Less Dev. -1.14 0 1.14