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Chapter 17

Chapter 17. Partial Correlation and Multiple Regression and Correlation. Chapter Outline. Introduction Partial Correlation Multiple Regression: Predicting the Dependent Variable Multiple Regression: Assessing the Effects of the Independent Variables. Chapter Outline. Multiple Correlation

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Chapter 17

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  1. Chapter 17 Partial Correlation and Multiple Regression and Correlation

  2. Chapter Outline • Introduction • Partial Correlation • Multiple Regression: Predicting the Dependent Variable • Multiple Regression: Assessing the Effects of the Independent Variables

  3. Chapter Outline • Multiple Correlation • Interpreting Statistics: Another Look at the Correlates of Crime • The Limitations of Multiple Regression and Correlation

  4. In This Presentation • Multiple regression • Using the multiple regression line to predict Y • Multiple correlation (R2)

  5. Introduction • Multiple Regression and Correlation allow us to: • Disentangle and examine the separate effects of the independent variables. • Use all of the independent variables to predict Y. • Assess the combined effects of the independent variables on Y.

  6. Multiple Regression Y = a + b1X1 + b2X2 • a = the Y intercept (Formula 17.6) • b1 =the partial slope of X1 on Y (Formula 17.4) • b2 =the partial slope of X2 on Y (Formula 17.5)

  7. Partial Slopes • The partial slopes = the effect of each independent variable on Y while controlling for the effect of the other independent variable(s). • Show the effects of the X’s in their original units. • These values can be used to predict scores on Y. • Partial slopes must be computed before computing a (the Y intercept).

  8. Formula 17.4 Formula 17.5 Formulas for Partial Slopes

  9. Formula for a • Formula 17.6

  10. Regression Coefficients for Problem 17.1 • The Y intercept (a) • Partial slopes: • a = 70.25 • b1 = 2.09 • b2 = -.43

  11. Standardized Partial Slopes(beta-weights) • Partial slopes (b1 and b2) are in the original units of the independent variables. • To compare the relative effects of the independent variables, compute beta-weights (b*). • Beta-weights show the amount of change in the standardized scores of Y for a one-unit change in the standardized scores of each independent variable while controlling for the effects of all other independent variables.

  12. Beta-weights • Use Formula 17.7 to calculate the beta-weight for X1 • Use Formula 17.8 to calculate the beta-weight for X2

  13. Beta-weights for Problem 17.1 • The Beta-weights show that the independent variables have roughly similar but opposite effects. • Turnout increases with unemployment and decreases with negative advertising.

  14. Multiple Correlation (R2) • The multiple correlation coefficient (R2) shows the combined effects of all independent variables on the dependent variable.

  15. Multiple Correlation (R2) • Formula 17.11 allows X1 to explain as much of Y as it can and then adds in the effect of X2 after X1 is controlled. • Formula 17.11 eliminates the overlap in the explained variance between X1 and X2.

  16. Multiple Correlation (R2) • Zero order correlation between unemployment (X1) and turnout. • r = .95 • X1 explains 90% (r2 = .90) of the variation in Y by itself.

  17. Multiple Correlation (R2) • Zero order correlation between neg. advert. (X2) and turnout. • r = - .87 • X2 explains 76% (r2 = .76) of the variation in Y by itself.

  18. Multiple Correlation (R2) • Unemployment (X1) explains 90%(r2 =.90) of the variance by itself. • R2 = .98 • To this, negative advertising (X2) adds 8% for a total of 98%.

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