Direction and Magnitude of Relationships

1
Direction and Magnitude of Relationships

• Positive Relationships
• Negligible Relationships
• Negative Relationships

2
Positive Relationship
3
Negligible Relationship
Circular Scatterplot
4
Negative Relationship
5
Two Continuous Variables
6
Scatterplot
(5, 5)
(4, 4)
(3, 3)
(2, 2)
(1, 1)
7
Coefficient of Correlation
8
Perfect Positive Linear Relationship
9
Two Continuous Variables
10
Scatterplot
11
Coefficient of Correlation
12
Positive Relationship
13
Two Continuous Variables
14
Scatterplot
15
Coefficient of Correlation
16
Negligible Relationship

• Given enough data, the scatterplot will
  approximate a circle.

17
Two Continuous Variables
18
Scatterplot
19
Coefficient of Correlation
20
Negative Relationship
21
Two Continuous Variables
22
Scatterplot
23
Coefficient of Correlation
24
Perfect Negative Relationship
25
Two Continuous Variables
26
Scatterplot
27
Non Linear Relationship
28
Coefficient of Correlation
?

• When the assumption of linearity is violated,
  Pearson's product moment coefficient of
  correlation will underestimate the strength of
  the relationship.