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

2. 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.

3. 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

4. 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

5. 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

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

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

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

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

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

11. 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

12. 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.

13. 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

14. 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.

15. 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.

16. 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

17. 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

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