After studying this chapter you will be able to: comprehend the nature of correlation analysis, understand bivariate regression analysis, become aware of the coefficient of determination, R2. Inviting you to refer.
AMBIENT/
Chủ đề:
Nội dung Text: Lecture Marketing research - Chapter 13: Bivariate correlation and regression
- Learning Objectives
CHAPTER Thirteen Bivariate
Correlation and
Regression
Copyright © 2004
John Wiley & Sons, Inc.
- Learning Objectives
Learning Objectives
1. To comprehend the nature of correlation
analysis.
2. To understand bivariate regression analysis.
3. To become aware of the coefficient of
determination, R2.
- Learning Objectives
Bivariate Analysis of To understand bivariate
Association regression analysis.
Bivariate Analysis Defined
The degree of association between two variables
Bivariate techniques
Statistical methods of analyzing the relationship
between two variables.
Multivariate Techniques
When more than two variables are involved
Independent variable
Affects the value of the dependent variable
Dependent variable
explained or caused by the independent variable
- Learning Objectives
Bivariate Analysis of To understand bivariate
Association 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
• Bivariate regression
• Pearson product moment correlation
- Learning Objectives
Bivariate Regression To understand bivariate
regression analysis.
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
• Nonlinear relationship
- Learning Objectives
Bivariate Regression To understand bivariate
regression analysis.
Bivariate Regression Example
Figure 13.1
Types of Relationships Found in Scatter Diagrams
Y
X
A - Strong Positive Linear Relationship
- Learning Objectives
Bivariate Regression To understand bivariate
regression analysis.
Figure 13.1
Types of Relationships Found in Scatter Diagrams
Y
X
B - Positive Linear Relationship
- Learning Objectives
Bivariate Regression To understand bivariate
regression analysis.
Figure 13.1
Types of Relationships Found in Scatter Diagrams
Y
X
C - Perfect Negative Linear Relationship
- Learning Objectives
Bivariate Regression To understand bivariate
regression analysis.
Figure 13.1
Types of Relationships Found in Scatter Diagrams
X
D - Perfect Parabolic Relationship
- Learning Objectives
Bivariate Regression To understand bivariate
regression analysis.
Figure 13.1
Types of Relationships Found in Scatter Diagrams
Y
X
E - Negative Curvilinear Relationship
- Learning Objectives
Bivariate Regression To understand bivariate
regression analysis.
Figure 13.1
Types of Relationships Found in Scatter Diagrams
Y
X
F - No Relationship between X and Y
- Learning Objectives
Bivariate Regression To understand bivariate
regression analysis.
Least Squares Estimation Procedure
Results in a straight line that fits the actual observations
better than any other line that could be fitted to the
observations.
Y = a + bX + e
where
Y = dependent variable
a = estimated Y intercept
b = estimated slope of the regression line
X = independent variable
e = error
- Learning Objectives
Bivariate Regression To understand bivariate
regression analysis.
Values for a and b can be calculated as
follows:
XiYi - nXY
b=
X2i - n(X)2
a = Y - bX
X = mean of value X
Y = mean of value y
n = sample size
- Learning Objectives
Bivariate Regression To become aware of the coefficient
of determination, R2.
The Regression Line
Predicted values for Y, based on calculated
values.
Strength of Association: R2
Coefficient of Determination, R2:
The measure of the strength of the linear
relationship between X and Y.
- Learning Objectives
Bivariate Regression To become aware of the coefficient
of determination, R2.
explained variance
R =
2
total variance
explained variance =
total variance - unexplained variance
total variance - unexplained variance
R = 2
total variance
unexplained variance
= 1-
total variance
- Learning Objectives
Bivariate Regression To become aware of the coefficient
of determination, R2.
unexplained variance
R =
2 1-
total variance
n
(Yi - Yi)2
I=1
= 1-
n
(Yi - Y)2
I=1
- Learning Objectives
Bivariate Regression To become aware of the coefficient
of determination, R2.
Statistical Significance of Regression Results
Total variation =
Explained variation + Unexplained variation
The total variation is a measure of variation of the observed
Y values around their mean.
It measures the variation of the Y values without any
consideration of the X values.
- Learning Objectives
Bivariate Regression To become aware of the coefficient
of determination, R2.
Total variation: Sum of squares (SST)
n
SST = (Yi - Y)2
i=1
n
n Yi
2
i=1
= Yi
2
i=1
n
- Learning Objectives
Bivariate Regression To become aware of the coefficient
of determination, R2.
Sum of squares due to regression (SSR)
n
SSR = (Yi - Y)2
i=1
n 2
n n Yi
i=1
= a i = 1Yi + bi = 1Xi Yi
n
- Learning Objectives
Bivariate Regression To become aware of the coefficient
of determination, R2.
Error sums of squares (SSE)
n
SSE = (Yi - Y)2
i=1
n n n
= Y2
i ai = 1Yi bi = 1XiYi
i=1
Thêm vào BST
Báo xấu
Download
Vui lòng tải xuống để xem tài liệu đầy đủ
