CORRELATION AND REGRESSION ANALYSIS
CHAPTER 13
CORRELATION AND REGRESSION ANALYSIS
OUTLINE
4.1 Definition of Correlation Analysis
4.2 Scatter Diagram and Types of Relationships
4.3 Correlation Coefficient
4.4 Interpretation of Correlation Coefficient
4.5 Definition of Regression Analysis
4.6 Dependent and Independent Variables
4.7 Simple Linear Regression: Least Squares Method
4.8 Using the simple Linear Regression equation
4.9 Cautionary Notes and Limitations
OBJECTIVES
By the end of this chapter, you will be able to:
1 determine the strength and nature of the association between the variables.
2 interpret the observed relationship between the variables of interest.
3 estimate possible outcome of an unknown variable upon the knowledge of the value of the variables and the relationship between the variables.
INTRODUCTION
By observation, we may notice that certain variables seem to be related or associated in some way and to some degree. For example, there may be relationships between number of hours spent on studying and the grades attained in examination; income earned and amount spent on entertainment.
Correlation Analysis and Regression Analysis are statistical techniques that study the relationships that exist between two or more variables. Such analyses are applied extensively in business, economics, psychology and science; and they are useful tools that can facilitate and improve decision makings.
4.1 DEFINITION OF CORRELATION ANALYSIS
Correlation Analysis is a technique that
Describes how the variables are related.
Measures the strength of the linear relationship between variables.
4.2 SCATTER DIAGRAM
It is a graph or chart on which we plot pairs of observed values for two variables which are denoted as X or Y
It gives two types of information:
. It tells whether or not two variables are related.
. if the variables are related, the type of relationship that exists between the variables concerned.
CORRELATION AND REGRESSION ANALYSIS
OUTLINE
4.1 Definition of Correlation Analysis
4.2 Scatter Diagram and Types of Relationships
4.3 Correlation Coefficient
4.4 Interpretation of Correlation Coefficient
4.5 Definition of Regression Analysis
4.6 Dependent and Independent Variables
4.7 Simple Linear Regression: Least Squares Method
4.8 Using the simple Linear Regression equation
4.9 Cautionary Notes and Limitations
OBJECTIVES
By the end of this chapter, you will be able to:
1 determine the strength and nature of the association between the variables.
2 interpret the observed relationship between the variables of interest.
3 estimate possible outcome of an unknown variable upon the knowledge of the value of the variables and the relationship between the variables.
INTRODUCTION
By observation, we may notice that certain variables seem to be related or associated in some way and to some degree. For example, there may be relationships between number of hours spent on studying and the grades attained in examination; income earned and amount spent on entertainment.
Correlation Analysis and Regression Analysis are statistical techniques that study the relationships that exist between two or more variables. Such analyses are applied extensively in business, economics, psychology and science; and they are useful tools that can facilitate and improve decision makings.
4.1 DEFINITION OF CORRELATION ANALYSIS
Correlation Analysis is a technique that
Describes how the variables are related.
Measures the strength of the linear relationship between variables.
4.2 SCATTER DIAGRAM
It is a graph or chart on which we plot pairs of observed values for two variables which are denoted as X or Y
It gives two types of information:
. It tells whether or not two variables are related.
. if the variables are related, the type of relationship that exists between the variables concerned.