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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 225 lecture 21

PS 225Lecture 21

Relationships between 3 or More Variables

relationships between multiple 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
Partial Correlation
  • Changes in a bivariate relationship when a third variable is introduced
  • Third variable (z) is a control variable
variable types
Variable Types
  • X
    • Interval-ratio
    • Independent
  • Y
    • Interval-ratio
    • Dependent
  • Z
    • Any level of measurement
    • Control
correlation coefficient
Correlation Coefficient
  • Rxy
  • Rxz
  • Rzy
  • Detailed notation for R
  • Relationship between 2 variables without incorporating third variable
  • Zero-order correlation
partial correlation coefficient
Partial Correlation Coefficient
  • Rxy,z
  • Detailed notation for R
  • Relationship between x and y controlling for z
  • First-order partials
types of relationships
Types of Relationships
  • Direct
  • Spurious
  • Intervening
  • Example: Possible relationship between geographic location, school performance and poverty
direct relationship
Direct Relationship

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

Y

X

spurious relationship
Spurious Relationship

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

X

Z

Y

intervening relationship
Intervening Relationship

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

Z

X

Y

determining relationship
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
Multiple Regression
  • Include any number of variable
  • Coefficients are partial slopes
  • Remove non-significant coefficients from the equation
spss assignment
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.
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