1. Learning Objective Chapter 14 Correlation and Regression Analysis CHAPTER fourteen Correlation and Regression Analysis Copyright © 2000 by John Wiley & Sons, Inc.

2. Learning Objective Chapter 14 Correlation and Regression Analysis Learning Objectives 1. To understand bivariate regression analysis. 2. To become aware of the coefficient of determination, R 2. 3. To comprehend the nature of correlation analysis.

3. Learning Objective Chapter 14 Correlation and Regression Analysis BIVARIATE ANALYSIS of ASSOCIATION Bivariate Analysis Defined The degree of association between two variables Bivariate techniques Statistical methods appropriate for bivariate analysis Independent variable Affects the value of the dependent variable To understand bivariate regression analysis.

4. Learning Objective Chapter 14 Correlation and Regression Analysis BIVARIATE ANALYSIS of ASSOCIATION Dependent variable Changes in response to the independent variable To understand bivariate regression analysis. Types of Bivariate Procedures Two group t-tests chi-square analysis of cross-tabulation or contingency tables ANOVA (analysis of variance) for two groups

5. Learning Objective Chapter 14 Correlation and Regression Analysis BIVARIATE REGRESSION Bivariate Regression Defined Analyzing the strength of the linear relationship between the dependent variable and the independent variable. Nature of the Relationship Plot in a scatter diagram Dependent variable: Y is plotted on the vertical axis Independent variable: X is plotted on the horizontal axis To understand bivariate regression analysis.

6. Learning Objective Chapter 14 Correlation and Regression Analysis Y X A - Strong Positive Linear Relationship BIVARIATE REGRESSION Figure 14.1 Types of Relationships Found in Scatter Diagrams

7. Learning Objective Chapter 14 Correlation and Regression Analysis Y X B - Positive Linear Relationship BIVARIATE REGRESSION Figure 14.1 Types of Relationships Found in Scatter Diagrams

8. Learning Objective Chapter 14 Correlation and Regression Analysis Y X C - Perfect Negative Linear Relationship BIVARIATE REGRESSION Figure 14.1 Types of Relationships Found in Scatter Diagrams

9. Learning Objective Chapter 14 Correlation and Regression Analysis Y X C - Perfect Parabolic Relationship BIVARIATE REGRESSION Figure 14.1 Types of Relationships Found in Scatter Diagrams

10. Learning Objective Chapter 14 Correlation and Regression Analysis Y X E - Negative Curvilinear Relationship BIVARIATE REGRESSION Figure 14.1 Types of Relationships Found in Scatter Diagrams

11. Learning Objective Chapter 14 Correlation and Regression Analysis Y X F - No Relationship between X and Y BIVARIATE REGRESSION Figure 14.1 Types of Relationships Found in Scatter Diagrams

12. Learning Objective Chapter 14 Correlation and Regression Analysis BIVARIATE REGRESSION Bivariate Regression Example Least Squares Estimation Procedure For fitting al line to data for X and Y Results in a straight line that fits the actual observations better than any other line that could be fitted to the observations. The Regression Line Predicted values for Y, based on calculated values. To understand bivariate regression analysis.

13. Learning Objective Chapter 14 Correlation and Regression Analysis BIVARIATE REGRESSION Strength of Association --- R 2 The coefficient of determination, R 2, is the measure of the strength of the linear relationship between X and Y. Statistical Significance of Regression Results To become aware of the coefficient of determination, R 2. total variation = explained variation + unexplained variation

14. Learning Objective Chapter 14 Correlation and Regression Analysis Hypotheses Concerning the Overall Regression Null Hypothesis H o : There is no linear relationship between X and Y. Alternative Hypothesis H a : There is a linear relationship between X and Y. To become aware of the coefficient of determination, R 2. BIVARIATE REGRESSION

15. Learning Objective Chapter 14 Correlation and Regression Analysis Hypotheses about the Regression Coefficient Null Hypothesis H o : b = 0 Alternative Hypothesis H a : b  0 The appropriate test is the t-test. To become aware of the coefficient of determination, R 2. BIVARIATE REGRESSION

16. Learning Objective Chapter 14 Correlation and Regression Analysis CORRELATION ANALYSIS Correlation for Metric Data - Pearson’s Product Moment Correlation Correlation analysis Analysis of the degree to which changes in one variable are associated with changes in another variable. Pearson’s product moment correlation Correlation analysis technique for use with metric data To comprehend the nature of correlation analysis.

17. Learning Objective Chapter 14 Correlation and Regression Analysis CORRELATION ANALYSIS Correlation Using Ordinal Data: Spearman’s Rank-Order Correlation To analyze the degree of association between two ordinally scaled variables. Correlation analysis technique for use with ordinal data. Conclusions regarding rankings: 1. Positively correlated 2. Negatively correlated 3. Independent To comprehend the nature of correlation analysis.

18. Learning Objective Chapter 14 Correlation and Regression Analysis The End Copyright © 2000 by John Wiley & Sons, Inc.