1. A researcher conducts a study to investigate the relationship between cigarette smoking and
illness. The number of cigarettes smoked daily and the number of days absent from work in the
last year due to illness are determined for 12 individuals. The scores are as follows:
Participant 1
2
3
4
5
6
7
8
9
10
11
12 #
Cigarettes
per day
0
0
0
10
13
20
27
35
35
44
53
60 Days
Absent
1
3
8
10
4
14
5
6
12
16
10
16 a. Which variable is the X variable (independent variable)…which is the Y (dependent
variable)?
b. Construct a scatter plot for the scores. Use Cigarettes Smoked as the X variable.
c. Find Zx , Zy (use N – 1 in your calculations of the standard deviation). Show your work in
the table provided.
d. Find the value of Pearson r (use N – 1 in your calculations of r). Show your work in the
table provided.
e. Interpret the correlation. Make sure to interpret the direction AND magnitude. 2. Which of the following statements concerning the linear correlation coefficient is/are true? In a
sentence for each, explain your answer.
a. If the linear correlation coefficient is .34, then the correlation accounts for
approximately 34% of the variance in the dependent variable.
b. If the slope of the regression line is negative, then the linear correlation coefficient is
negative.
c. The value of the linear correlation coefficient always lies between -1 and 1, but the
coefficient of determination can take on any value.
d. A linear correlation coefficient of 0.62 suggests a stronger linear relationship than a
linear correlation coefficient of -0.82.
3. Answer the questions below using the following correlation table: GRE Math
GRE Verbal
IQ
GPA
GRE Math
1.00
.34
.23
.48
GRE Verbal
-1.00
.67
.39
IQ
–1.00 .82
GPA
—1.00
a. Which one of the variables (GRE math, GRE verbal, IQ) has the strongest correlation
with GPA?
b. What percentage of the variance in GPA can be explained by GRE Math?
4. A clinical psychologist is interested in the relationship between testosterone in married males
and their marital satisfaction. Data for 8 participants are listed below:
Participant
1
2
3
4
5
6
7
8 Testosterone
Level
12
13
19
25
9
16
15
21 Relationship
Satisfaction
24
15
15
10
19
11
20
19 a. Examine the data and predict the sign associated with the slope of the regression line.
Explain your response.
b. Determine the least squares regression line using Testosterone as the IV. Show your
work in the table provided. 5. The regression equation relating attitude rating (x) and job performance rating (y) for ten
randomly selected employees of a company is y = 1.02x + 11.7. Predict the job performance
rating for an employee whose attitude rating is 68. 6. A scientist with the environmental protection agency wants to determine whether there is an
association between cancer mortality and pollution. She collects the following rank data for 20
different cities:
City
Pollution
Cancer
Rank
Rank
1
1
1
2
4
7
3
8
10
4
11
14
5
15
18
6
5
2
7
14
6
8
2
11
9
6
15
10
