1. A city wants to see if there is a linear relationship between property tax and
annual income of its residents. A random sample of seven residents was
selected with the following results:
Property Tax in
thousands of dollars (X)
3.5
5.2
9.4
7.1
1.2
15.8
6.3
Annual Income thousands
of dollars (Y)
55
65
125
102
23
205
85
2. A county relief organization wants to determine if there is a linear relationship
between the number of children and annual household income in thousands of
dollars.
Number of children (X)
3
6
2
5
1
2
4
Annual Income thousands
of dollars (Y)
47
21
75
30
94
81
35
3. A fraternity at a large university wanted to determine if there is a linear
relationship between the number of alcoholic beverages consumed per week
not including weekends and the grade point average (GPA) of its members.
Number of Alcoholic
Beverages Consumed (X)
4
18
7
0
10
6
12
3
15
Grade Point Average (Y)
3.8
2.3
3.5
3.7
2.8
4.0
3.2
3.6
2.9
4. A psychologist wants to find out if there is a linear relationship between the
number of sunny days in a year and positive attitude. The psychologist
measures positive attitude on a 100 point scale where a score of 100 indicates
the highest possible positive attitude and 0 indicates a completely negative
attitude (or the lowest possible positive attitude).
Number of Sunny Days (X)
240
315
142
85
330
220
123
98
57
Psychologists Attitude Test (Y)
73
89
65
25
68
78
81
58
32
8.5 Correlation
page 372
By Will Tenney
5. A high school soccer coach wants to determine if there is a linear relationship
between the number of days of practice and the number of wins in a season.
She compares wins and days of practice for her last six seasons.
Number of Days of
Practice (X)
45
56
48
60
52
58
Number of Wins (Y)
5
8
9
5
7
8
6.
A regional manager for McDonald’s believes that there is a linear relationship between
a town’s population and the number of successful McDonald’s franchises in a town.
Population in tens of
thousands (X)
25
37
6
15
11
9
53
3
28
Number of successful
franchises (Y)
12
17
3
14
7
3
21
4
17
For the following problems, consider the following scatter plots:
A
B
C
D
E
0
5
10
15
0
5
10
15
0
5
10
15
20
0
5
10
15
0
5
10
0
10
20
0
5
10
15
0
5
10
15
0
5
10
15
0
5
10
15
8.5 Correlation
page 373
By Will Tenney
State which graph has the following correlation coefficient.
7.
r = 0.82
8.
r = -1.00
9.
r = - 0.72
10.
r = 1.00
11.
r = 0.08
For the following problems you may use a calculator that finds the correlation
coefficient or the formula. It is easier and quicker to use a calculator with the
correlation coefficient feature.
