
How do you test the covariation between
two variables?

Most typically:

One independent variable

and:

One dependent variable
Marketing Research
7/17/2016
2
Types of Relationships
Scatterplot Diagrams
Y
Y
X
X
No Apparent Relationship Between X and Y
Perfect Positive Relationship Between X and Y
Y
Y
X
Perfect Negative Relationship Between X and Y
X
Parabolic Relationship Between X and Y
3
Types of Relationships
Scatterplot Diagrams
Y
Y
X
General Negative Relationship Between X and Y
X
General Positive Relationship Between X and Y
Y
Y
X
Negative Curvilinear Relationship Between X and Y
X
No Apparent Relationship Between X and Y
4
Marketing Research
7/17/2016
5
Marketing Research
7/17/2016
6
Marketing Research
7/17/2016
7

examines the strength of the relationship
between two continuous variables

range:
◦ between -1 (perfect inverse relationship),
◦ through 0 (no relationship at all)
◦ to +1 (perfect positive relationship)
Marketing Research
7/17/2016
8
Marketing Research
7/17/2016
9
Marketing Research
7/17/2016
10
Marketing Research
7/17/2016
11
Marketing Research
7/17/2016
12
Marketing Research
7/17/2016
13
Marketing Research
7/17/2016
14
Correlation
Assessing Measures of Association
Measure of Association using interval or ratio data.
Measure of Association using ordinal or rank order data.
15

How do you test the covariation between

one continuous independent variable
◦ (e.g., age, income)

and:

one continuous dependent variable
◦ (e.g., cost of automobile purchased)
Marketing Research
7/17/2016
16
Least-Square Estimation Procedure
• Used to fit data for X and Y
• Enables estimation of non-plotted data points
• Results in a straight line that fits the actual observations (plotted
dots) better than any other line that could be fit to the observations.
Y
X
17
Liquor
Consumption
# Churches
Correlations
EXAM_1
EXAM_2
REVIEW_1
Pears on Correlation
Sig. (1-tailed)
N
Pears on Correlation
Sig. (1-tailed)
N
Pears on Correlation
Sig. (1-tailed)
N
EXAM_1
1.000
.
42
.334*
.015
42
.226
.075
42
EXAM_2
REVIEW_1
.334*
.226
.015
.075
42
42
1.000
.438**
.
.002
42
42
.438**
1.000
.002
.
42
42
*. Correlation is s ignificant at the 0.05 level (1-tailed).
**. Correlation is s ignificant at the 0.01 level (1-tailed).
Marketing Research
7/17/2016
19

Yi = B0 + B1 X1 + ei
◦ Y is the dependent variable (estimated outcome)
◦ B0 is the value of Y when X = 0 (the Y intercept)
◦ B1 is the rate at which Y changes for every unit
change in X (the slope)
◦ and e is the error in the model
Marketing Research
7/17/2016
20

Test statistic:

H0: B1 = 0

Ha: B1 does not = 0
Marketing Research
7/17/2016
21
Marketing Research
7/17/2016
22
Coefficientsa
Unstandardized
Coefficients
Model
1
(Constant)
EXAM_1
B
51.344
.291
Std. Error
10.047
.130
Standardized
Coefficients
Beta
.334
t
5.110
2.242
Sig.
.000
.031
a. Dependent Variable: EXAM_2
Marketing Research
7/17/2016
23
24