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Understanding Measures of Association: Correlation and Regression Analysis

This chapter delves into measures of association, focusing on correlation analysis and regression. Learn how to study relationships among variables using Pearson's Product Moment Correlation coefficient, and discover the use of regression analysis with least squares to create the best fit line for predictions. It covers requirements for testing linearity, assessing regression model effectiveness, and exploring nonparametric alternatives. Gain insights into interpreting coefficients and understanding the practical significance in the context of data relationships.

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Understanding Measures of Association: Correlation and Regression Analysis

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  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 19-9 Comparison of Bivariate Linear Correlation and Regression

  16. Exhibit 19-10 Examples of Different Slopes

  17. Concept Application

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

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

  20. Exhibit 19-14 Wine Price Study Example

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

  22. Exhibit 19-16 Plot of Standardized Residuals

  23. Exhibit 19-17 Prediction and Confidence Bands

  24. 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

  25. Exhibit 19-18 Components of Variation

  26. Exhibit 19-19 F Ratio in Regression

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

  28. Exhibit 19-20 Chi-Square Based Measures

  29. Exhibit 19-21Proportional Reduction of Error Measures

  30. Exhibit 19-22 Statistical Alternatives for Ordinal Measures

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

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

  33. 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

  34. 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

  35. Intercept Slope Residual Scatterplot Simple prediction tau Key Terms

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