PS 225 Lecture 21

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# PS 225 Lecture 21 - PowerPoint PPT Presentation

PS 225 Lecture 21. Relationships between 3 or More Variables. Relationships Between Multiple Variables. Three or more variables can be interrelated Confounding variables Example: Individuals given the medication Lipitor are more likely to die of a heart attack. Partial Correlation.

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### PS 225Lecture 21

Relationships between 3 or More Variables

Relationships Between Multiple Variables
• Three or more variables can be interrelated
• Confounding variables
• Example: Individuals given the medication Lipitor are more likely to die of a heart attack
Partial Correlation
• Changes in a bivariate relationship when a third variable is introduced
• Third variable (z) is a control variable
Variable Types
• X
• Interval-ratio
• Independent
• Y
• Interval-ratio
• Dependent
• Z
• Any level of measurement
• Control
Correlation Coefficient
• Rxy
• Rxz
• Rzy
• Detailed notation for R
• Relationship between 2 variables without incorporating third variable
• Zero-order correlation
Partial Correlation Coefficient
• Rxy,z
• Detailed notation for R
• Relationship between x and y controlling for z
• First-order partials
Types of Relationships
• Direct
• Spurious
• Intervening
• Example: Possible relationship between geographic location, school performance and poverty
Direct Relationship

X causes changes in Y. Rxy and Rxy,z are similar.

Y

X

Spurious Relationship

Z has a relationship with both the independent and dependent variable. Rxy and Rxy,z are different

X

Z

Y

Intervening Relationship

Z has a relationship with both the independent and dependent variable. Rxy and Rxy,z are different.

Z

X

Y

Determining Relationship
• Establish existence of a relationship between independent (x) and Dependent (y) variables
• Explore relationship between x, y and any associated confounding variables (z)
• Calculate partial correlation coefficient and identify relationship type
Multiple Regression
• Include any number of variable
• Coefficients are partial slopes
• Remove non-significant coefficients from the equation
SPSS Assignment

Last class we answered the following questions:

• Does the number of years of education an individual has affect the hours of television a person watches?
• Does age affect the hours of television a person watches?

This class: Use SPSS to find the regression equation that best represents the relationship between age and hours of television a person watches. Treat years of education as a confounding variable.

• Give the relationship between each pair of variables.
• Calculate the partial correlation coefficient. What is the most probable relationship type between variables?
• Give the multiple regression equation and predict the number of hours of television you watch. Compare the prediction to the actual number of hours.