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PS 225 Lecture 21

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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  1. PS 225Lecture 21 Relationships between 3 or More Variables

  2. 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

  3. Partial Correlation • Changes in a bivariate relationship when a third variable is introduced • Third variable (z) is a control variable

  4. Variable Types • X • Interval-ratio • Independent • Y • Interval-ratio • Dependent • Z • Any level of measurement • Control

  5. Correlation Coefficient • Rxy • Rxz • Rzy • Detailed notation for R • Relationship between 2 variables without incorporating third variable • Zero-order correlation

  6. Partial Correlation Coefficient • Rxy,z • Detailed notation for R • Relationship between x and y controlling for z • First-order partials

  7. Types of Relationships • Direct • Spurious • Intervening • Example: Possible relationship between geographic location, school performance and poverty

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

  9. Spurious Relationship Z has a relationship with both the independent and dependent variable. Rxy and Rxy,z are different X Z Y

  10. Intervening Relationship Z has a relationship with both the independent and dependent variable. Rxy and Rxy,z are different. Z X Y

  11. 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

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

  13. 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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