# Chapter 19

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## Chapter 19

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##### Presentation Transcript

1. Chapter 19 Measures of Association

2. Learning Objectives Understand . . . • how correlation analysis may be applied to study relationships between two or more variables • uses, requirements, and interpretation of the product moment correlation coefficient • how predictions are made with regression analysis using the method of least squares to minimize errors in drawing a line of best fit

3. Learning Objectives Understand . . . • how to test regression models for linearity and whether the equation is effective in fitting the data • nonparametric measures of association and the alternatives they offer when key assumptions and requirements for parametric techniques cannot be met

4. Exhibit 19-1 Measures of Association: Interval/Ratio

5. Exhibit 19-1 Measures of Association: Ordinal

6. Exhibit 19-1 Measures of Association: Nominal

7. Relationships “To truly understand consumers’ motives and actions, you must determine relationships between what they think and feel and what they actually do.” David Singleton, Vice President of Insights, Zyman Marketing Group

8. Pearson’s Product Moment Correlation r Is there a relationship between X and Y? What is the magnitude of the relationship? What is the direction of the relationship?

9. Exhibit 19-2 Scatterplots of Relationships

10. Exhibit 19-4 Scatterplots

11. Exhibit 19-7 Diagram of Common Variance

12. Interpretation of Correlations X causes Y Y causes X X and Y are activated by one or more other variables X and Y influence each other reciprocally

13. Exhibit 19-8 Artifact Correlations

14. Interpretation of Coefficients A coefficient is not remarkable simply because it is statistically significant! It must be practically meaningful.

15. Exhibit 19-10 Examples of Different Slopes

16. Concept Application

17. Exhibit 19-11 Plot of Wine Price by Average Temperature

18. Exhibit 19-12 Distribution of Y for Observation of X

19. Exhibit 19-14 Wine Price Study Example

20. Exhibit 19-15 Least Squares Line: Wine Price Study

21. Exhibit 19-16 Plot of Standardized Residuals

22. Exhibit 19-17 Prediction and Confidence Bands

23. Testing Goodness of Fit Y is completely unrelated to X and no systematic pattern is evident There are constant values of Y for every value of X The data are related but represented by a nonlinear function

24. Exhibit 19-18 Components of Variation

25. Exhibit 19-19 F Ratio in Regression

26. Coefficient of Determination: r2 Total proportion of variance in Y explained by X Desired r2: 80% or more

27. Exhibit 19-20 Chi-Square Based Measures

28. Exhibit 19-21Proportional Reduction of Error Measures

29. Exhibit 19-22 Statistical Alternatives for Ordinal Measures

30. Exhibit 19-23 Calculation of Concordant (P), Discordant (Q), Tied (Tx,Ty), and Total Paired Observations:KeyDesign Example

31. Exhibit 19-24 KDL Data for Spearman’s Rho

32. Artifact correlations Bivariate correlation analysis Bivariate normal distribution Chi-square-based measures Contingency coefficient C Cramer’s V Phi Coefficient of determination (r2) Concordant Correlation matrix Discordant Error term Goodness of fit lambda Key Terms

33. Linearity Method of least squares Ordinal measures Gamma Somers’s d Spearman’s rho tau b tau c Pearson correlation coefficient Prediction and confidence bands Proportional reduction in error (PRE) Regression analysis Regression coefficients Key Terms

34. Intercept Slope Residual Scatterplot Simple prediction tau Key Terms