learning objective chapter 14 correlation and regression analysis chapter fourteen correlation and...
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Learning ObjectiveLearning ObjectiveChapter 14Chapter 14
Correlation and Regression Analysis
CHAPTER fourteen
Correlation and
Regression Analysis
Copyright © 2000 by John Wiley & Sons, Inc.
Learning ObjectiveLearning ObjectiveChapter 14Chapter 14
Correlation and Regression Analysis
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.
Learning ObjectiveLearning ObjectiveChapter 14Chapter 14
Correlation and Regression Analysis
BIVARIATE ANALYSIS of ASSOCIATION
BIVARIATE ANALYSIS of ASSOCIATION
Bivariate Analysis DefinedThe 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.
Learning ObjectiveLearning ObjectiveChapter 14Chapter 14
Correlation and Regression Analysis
BIVARIATE ANALYSIS of ASSOCIATION
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
Learning ObjectiveLearning ObjectiveChapter 14Chapter 14
Correlation and Regression Analysis
BIVARIATE REGRESSIONBIVARIATE 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.
Learning ObjectiveLearning ObjectiveChapter 14Chapter 14
Correlation and Regression Analysis
Y
XA - Strong Positive Linear Relationship
BIVARIATE REGRESSIONBIVARIATE REGRESSION
Figure 14.1Types of Relationships Found in Scatter Diagrams
Learning ObjectiveLearning ObjectiveChapter 14Chapter 14
Correlation and Regression Analysis
Y
X
B - Positive Linear Relationship
BIVARIATE REGRESSIONBIVARIATE REGRESSION
Figure 14.1Types of Relationships Found in Scatter Diagrams
Learning ObjectiveLearning ObjectiveChapter 14Chapter 14
Correlation and Regression Analysis
Y
XC - Perfect Negative Linear Relationship
BIVARIATE REGRESSIONBIVARIATE REGRESSION
Figure 14.1Types of Relationships Found in Scatter Diagrams
Learning ObjectiveLearning ObjectiveChapter 14Chapter 14
Correlation and Regression Analysis
Y
XC - Perfect Parabolic Relationship
BIVARIATE REGRESSIONBIVARIATE REGRESSION
Figure 14.1Types of Relationships Found in Scatter Diagrams
Learning ObjectiveLearning ObjectiveChapter 14Chapter 14
Correlation and Regression Analysis
Y
XE - Negative Curvilinear Relationship
BIVARIATE REGRESSIONBIVARIATE REGRESSION
Figure 14.1Types of Relationships Found in Scatter Diagrams
Learning ObjectiveLearning ObjectiveChapter 14Chapter 14
Correlation and Regression Analysis
Y
X
F - No Relationship between X and Y
BIVARIATE REGRESSIONBIVARIATE REGRESSION
Figure 14.1Types of Relationships Found in Scatter Diagrams
Learning ObjectiveLearning ObjectiveChapter 14Chapter 14
Correlation and Regression Analysis
BIVARIATE REGRESSIONBIVARIATE 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.
Learning ObjectiveLearning ObjectiveChapter 14Chapter 14
Correlation and Regression Analysis
BIVARIATE REGRESSIONBIVARIATE 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
To become aware of the coefficient of determination, R2.
total variation =
explained variation + unexplained variation
Learning ObjectiveLearning ObjectiveChapter 14Chapter 14
Correlation and Regression Analysis
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.
To become aware of the coefficient of determination, R2.
BIVARIATE REGRESSIONBIVARIATE REGRESSION
Learning ObjectiveLearning ObjectiveChapter 14Chapter 14
Correlation and Regression Analysis
Hypotheses about the Regression Coefficient
Null Hypothesis Ho:
b = 0
Alternative Hypothesis Ha:
b 0
The appropriate test is the t-test.
To become aware of the coefficient of determination, R2.
BIVARIATE REGRESSIONBIVARIATE REGRESSION
Learning ObjectiveLearning ObjectiveChapter 14Chapter 14
Correlation and Regression Analysis
CORRELATION ANALYSISCORRELATION 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.
Learning ObjectiveLearning ObjectiveChapter 14Chapter 14
Correlation and Regression Analysis
CORRELATION ANALYSISCORRELATION 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.
Learning ObjectiveLearning ObjectiveChapter 14Chapter 14
Correlation and Regression Analysis
The End
Copyright © 2000 by John Wiley & Sons, Inc.