PS 225 Lecture 21 Relationships between 3 or More Variables.
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Transcript of PS 225 Lecture 21 Relationships between 3 or More Variables.
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PS 225Lecture 21
Relationships between 3 or More Variables
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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
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Partial Correlation
Changes in a bivariate relationship when a third variable is introduced
Third variable (z) is a control variable
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Variable Types
X Interval-ratio Independent
Y Interval-ratio Dependent
Z Any level of measurement Control
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Correlation Coefficient
Rxy
Rxz
Rzy
Detailed notation for R Relationship between 2 variables
without incorporating third variable Zero-order correlation
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Partial Correlation Coefficient
Rxy,z
Detailed notation for R Relationship between x and y controlling
for z First-order partials
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Types of Relationships
Direct Spurious Intervening
Example: Possible relationship between geographic location, school performance and poverty
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Direct Relationship
X causes changes in Y. Rxy and Rxy,z are similar.
X Y
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Spurious Relationship
Z has a relationship with both the independent and dependent variable. Rxy and Rxy,z are different
ZX
Y
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Intervening Relationship
Z has a relationship with both the independent and dependent variable. Rxy and Rxy,z are different.
Z
X Y
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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
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Multiple Regression
Include any number of variable
Coefficients are partial slopes Remove non-significant coefficients
from the equation
2211 xbxbay
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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.