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Figure 18.1 Relationship of Correlation and Regression to the
Previous Chapters and the Marketing Research Process
Focus of This
Chapter
• Correlation
• Regression
Relationship to
Previous Chapters
• Analytical
Framework and
Models
(Chapter 2)
• Data Analysis
Strategy
(Chapter 15)
• General Procedure
of Hypothesis
Testing
(Chapter
16)
• Hypothesis Testing
Related to
Differences
(Chapter 17)
Relationship to Marketing
Research Process
Problem Definition
Approach to Problem
Research Design
Field Work
Data Preparation
and Analysis
Report-Preparation
and Presentation
Figure 18.2 Correlation and Regression: An Overview
Product Moment Correlation
Fig 18.3-18.4
Table 18.1
Regression Analysis
Bivariate Regression
Figs 18.5-18.7
Table 18.2
Multiple Regression
Table 18.3
Application to Contemporary Issues
TQM
International
Technology
Ethics
Focus on Elrick & Lavidge
Internet Applications
Opening Vignette
Figure 18.3 Plot of Attitude With Duration of Car Ownership
Figure 18.4 A Nonlinear Relationship for Which r = 0
6
.
.
.
5
4
.
.
3
2
.
1
0
-3
.
-2
-1
0
1
2
3
Figure 18.5 Conducting Bivariate Regression Analysis
Opening Vignette
Focus on Elrick & Lavidge
Internet Applications
Scatter Diagram
General Model
Estimation of Parameters
Standardized Regression Coefficient
Application to Contemporary Issues
TQM
International
Technology
Ethics
Figure 18.5 Conducting Bivariate Regression Analysis (continued)
Opening Vignette
Focus on Elrick & Lavidge
Internet Applications
Significance Testing
Strength and Significance of Association
Prediction Accuracy
Examination of Residuals
Application to Contemporary Issues
TQM
International
Technology
Ethics
Figure 18.6 Bivariate Regression
Y
b0 + b1 X
Figure 18.7 Decomposition of the Total Variation In
Bivariate Regression
Y
{
Total variation,
SSY
}
}
Residual variation,
SS RES
Explained variation,
SS REG
Y
X
Figure 18.8 Other Computer Programs for Correlations
SAS
CORR produces metric and nonmetric correlations between variables,
including Pearson’s product moment correlation.
MINITAB
Correlation can be computed using STAT>BASICSTATISTICS>
CORRELATION function. It calculates Pearson’s product moment using
all the columns.
EXCEL
Correlations can be determined in EXCEL by using the TOOLS>DATA
ANALYSIS>CORRELATION function. Use the Correlation Worksheet
Function when a correlation coefficient for two cell ranges is needed.
Figure 18.8 Other Computer Programs for Regression
SAS
REG is a general purpose regression procedure that fits bivariate and multiple regression models
using the least-squares procedures. All the associated statistics are computed, and residuals can be
plotted.
MINITAB
Regression analysis under the STATS>REGRESSIOIN function can perform simple and multiple
analysis. The output includes a linear regression equation, table of coefficients R square, R
squared adjusted, analysis of variance table, a table of fits and residuals that provide unusual
observations. Other available features include fitted line plot, and residual plots.
EXCEL
Regression can be assessed from the TOOLS>DATA ANALYSIS menu. Depending on the
features selected, the output can consist of a summary output table, including an ANOVA table, a
standard error of y estimate, coefficients, standard error of coefficients, R2 values, and the number
of observations. In addition, the function computes a residual output table, a residual plot, a line
fit plot, normal probability plot, and a two-column probability data output table.
TABLE 18.1
EXPLAINING ATTITUDE TOWARD SPORTS CARS
______________________________________________________________
Respondent
No
1
Attitude
Toward
Sports Cars
6
Duration
of Sports Car
Ownership
10
Importance
Attached to
Performance
3
2
9
12
11
3
8
12
4
4
3
4
1
5
10
12
11
6
4
6
1
7
5
8
7
8
2
2
4
9
11
18
8
10
9
9
10
11
10
17
8
12
2
2
5
TABLE 18.2
BIVARIATE REGRESSION
Multiple R
.9361
R2
.8762
Adjusted R2
.8639
Standard Error
1.2233
Analysis of Variance
df
Sum of Squares
Mean Square
Regression
1
105.9522
105.9522
Residual
10
14.9644
1.4964
F =
70.8027
Significance of F =
.0000
VARIABLES IN THE EQUATION
Variable
b
SE b
Beta (B)
T
Sig. T
Duration
.5897
.0700
.9361
8.414
.0000
(Constant)
1.0793
.7434
1.452
.1772
TABLE 18.3
MULTIPLE REGRESSION
Multiple R
.9721
R2
.9450
Adjusted R2
.9330
Standard Error
.8597
Analysis of Variance
df
Sum of Squares
Mean Square
Regression
2
114.2643
57.1321
Residual
9
6.6524
.7392
F =
77.2936
Significance of F =
.0000
VARIABLES IN THE EQUATION
Variable
b
SE b
Beta (B)
T
Sig. T
Importance
.2887
.08608
.3138
3.353
.0085
Duration
.4811
.05895
.7636
8.160
.0000
(Constant)
.3373
.56736
.595
.5668