CHAPTER fourteen Correlation and Regression Analysis Copyright © 2000 South-Western College Publishing Co.

Learning Objectives 1. To understand bivariate regression analysis. 2. To become aware of the coefficient of determination, R2. 3. To comprehend the nature of correlation analysis.

Bivariate Analysis Defined To understand bivariate 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

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

Bivariate Regression Defined To understand bivariate 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

A - Strong Positive Linear Relationship Figure 14.1 Types of Relationships Found in Scatter Diagrams BIVARIATE REGRESSION Y X A - Strong Positive Linear Relationship

B - Positive Linear Relationship Figure 14.1 Types of Relationships Found in Scatter Diagrams BIVARIATE REGRESSION Y X B - Positive Linear Relationship

C - Perfect Negative Linear Relationship Figure 14.1 Types of Relationships Found in Scatter Diagrams BIVARIATE REGRESSION Y X C - Perfect Negative Linear Relationship

C - Perfect Parabolic Relationship Figure 14.1 Types of Relationships Found in Scatter Diagrams BIVARIATE REGRESSION Y X C - Perfect Parabolic Relationship

E - Negative Curvilinear Relationship Figure 14.1 Types of Relationships Found in Scatter Diagrams BIVARIATE REGRESSION Y X E - Negative Curvilinear Relationship

F - No Relationship between X and Y Figure 14.1 Types of Relationships Found in Scatter Diagrams BIVARIATE REGRESSION Y X F - No Relationship between X and Y

Bivariate Regression Example Least Squares Estimation Procedure To understand bivariate 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.

Strength of Association --- R2 To become aware of the coefficient of determination, R2. BIVARIATE REGRESSION Strength of Association --- R2 The coefficient of determination, R2, is the measure of the strength of the linear relationship between X and Y. Statistical Significance of Regression Results total variation = explained variation + unexplained variation

Hypotheses Concerning the Overall Regression To become aware of the coefficient of determination, R2. BIVARIATE REGRESSION Hypotheses Concerning the Overall Regression Null Hypothesis Ho: There is no linear relationship between X and Y. Alternative Hypothesis Ha: There is a linear relationship between X and Y.

Hypotheses about the Regression Coefficient To become aware of the coefficient of determination, R2. BIVARIATE REGRESSION Hypotheses about the Regression Coefficient Null Hypothesis Ho: b = 0 Alternative Hypothesis Ha: b  0 The appropriate test is the t-test.

Correlation for Metric Data - Pearson’s Product Moment Correlation To comprehend the nature of correlation 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

Correlation Using Ordinal Data: Spearman’s Rank-Order Correlation To comprehend the nature of correlation 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

The End Copyright © 2000 South-Western College Publishing Co.