PS 225 Lecture 21 - PowerPoint PPT Presentation

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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

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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.