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.

X Y

Spurious Relationship

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

ZX

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

1. Establish existence of a relationship between independent (x) and Dependent (y) variables

2. Explore relationship between x, y and any associated confounding variables (z)

3. 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

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SPSS AssignmentLast 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.