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## PowerPoint Slideshow about ' PS 225 Lecture 21' - byron-harper

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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

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.

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