The Pearson r and Spearman rho correlation coefficients are related measures of the strength and direction of association between two variables. The Pearson r assumes a linear relationship while the Spearman rho does not, making it a nonparametric alternative. A professor administered two exams to students and collected their scores to determine if exam 1 scores correlated with exam 2 scores. An analysis of the data from 8 students found a positive linear relationship between their scores on the two exams.

1. 10. The Pearson r and Spearman rho correlation coefficients are
related. Is this statement correct? Explain.
15. In a large introductory sociology course, a professor gives
two exams. The professor wants to determine whether the scores
students receive on the second exam are correlated with their
scores on the first exam. To make the calculations easier, a
sample of eight students is selected. Their scores are shown in
the accompanying table.
Student Exam 1 Exam 2
1 60 60
2 75 100
3 70 80
4 72 68
5 54 73
6 83 97
7 80 85
8 65 90
a. Construct a scatter plot of the data, using exam 1 score as the
X variable. Does the relationship look linear?
b. Assuming a linear relationship exists between scores on the
two exams, compute the value for Pearson r.
c. How well does the relationship account for the scores on
exam 2?
18. An educator has constructed a test for mechanical aptitude.
He wants to determine how reliable the test is over two

2. administrations spaced by 1 month. A study is conducted in
which 10 students are given two administrations of the test,
with the second administration being 1 month after the first.
The data are given in the following table.
Student Administration 1 Administration 2
1 10 10
2 12 15
3 20 17
4 25 25
5 27 32
6 35 37
7 43 40
8 40 38
9 32 30
10 47 49
a. Construct a scatter plot of the paired scores.
b. Determine the value of r.
c. Would it be fair to say that this is a reliable test? Explain
using r2.
22. A social psychologist conducts a study to determine the
relationship between religion and selfesteem. Ten eighth
graders are randomly selected for the study. Each individual
undergoes two tests, one measuring self-esteem and the other
religious involvement. For the self-esteem test, the lower the
score is, the higher self-esteem is; for the test measuring
religious involvement, the higher the score is, the higher

3. religious involvement is. The selfesteem test has a range from 1
to 10 and the religious involvement test ranges from 0 to 50.
For the purposes of this question, assume both tests are well
standardized and of interval scaling. The following data are
collected.
Subject Religious Involvement Self-Esteem
1 5 8
2 25 3
3 45 2
4 20 7
5 30 5
6 40 5
7 1 4
8 15 4
9 10 7
10 35 3
a. If a relationship exists such that the more religiously
involved one is, the higher actual self-esteem is, would you
expect r computed on the provided values to be negative or
positive? Explain.
b. Compute r. Were you correct in your answer to part a?
Chapter 7:
9. Given the set of paired X and Y scores,
X 7 10 9 13 7 11 13
Y 1 2 4 3 3 4 5
a. Construct a scatter plot of the paired scores. Does the
relationship appear linear?
b. Determine the least-squares regression line for predicting Y
given X.

4. c. Draw the regression line on the scatter plot.
d. Using the relationship between X and Y, what value would
you predict for Y if X 12? (Round to two decimal places.)
The predicted Y is,
12. A statistics professor conducts a study to investigate the
relationship between the performance of his studentson exams
and their anxiety. Ten students fromhis class are selected for the
experiment. Just before taking the final exam, the 10 students
are given ananxiety questionnaire. Here are final exam and
anxietyscores for the 10 students:
Student No.1 2 3 4 5 6 7 89 10
Anxiety 28 4135 39 31 42 50 46 45 37
Final Exam 82 5863 89 92 64 55 70 51 72
a. On a piece of graph paper, construct a scatter plot of the
paired scores. Use anxiety as the X variable.
b. Describe the relationship shown in the graph.
c. Assuming the relationship is linear, compute the value of
Pearson r.
d. Determine the least-squares regression line for predicting the
final exam score, given the anxiety level. Should be Y be
positive or negative? Why?
SUMMARY OUTPUT

5. Regression Statistics
Multiple R
0.6908
R Square
0.4772
Adjusted R Square
0.4118

6. Standard Error
10.8653
Observations
10
ANOVA
df
SS
MS

7. F
Significance F
Regression
1
861.9592
861.9592
7.3013
0.0270
Residual
8
944.4408
118.0551
Total
9
1806.4000
Coefficients
Standard Error
t Stat
P-value

8. Lower 95%
Upper 95%
Intercept
125.8830
21.1109
5.9629
0.0003
77.2013
174.5648
Anxiety
-1.4285
0.5287
-2.7021
0.0270
-2.6476
-0.2094
e. Draw the least-squares regression line of part d on the scatter
plot of part a.
f. Based on the data of the 10 students, if a student has an
anxiety score of 38, what value would you predict for her final
exam score? (Round to two decimal places.)
g. Calculate the standard error of estimate for predicting final
exam scores from anxiety scores.
13. The sales manager of a large sporting goods store
hasrecently started a national advertising campaign. Hehas kept
a record of the monthly costs of the advertisingand the monthly
profits. These are shown here The entries are in thousands of

9. dollars.
Month Jan.Feb.Mar.Apr.May Jun. Jul.
MonthlyAdvertising Cost10.0 14.011.4 15.6 16.8 11.2 13.2
Monthly Profit125 200160 150 210 110 125
a. Assuming a linear relationship exists, derive the least-squares
regression line for predicting monthly profits from monthly
advertising costs.
SUMMARY OUTPUT
Regression Statistics
Multiple R
0.6958

10. R Square
0.4841
Adjusted R Square
0.3809
Standard Error
30.3395
Observations
7

11. ANOVA
df
SS
MS
F
Significance F
Regression
1
4318.9930
4318.9930
4.6921
0.0825
Residual
5
4602.4356
920.4871
Total
6
8921.4286

12. Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Intercept
11.6599
66.8350
0.1745
0.8683
-160.1449
183.4648
Monthly Advertising Cost
10.8284
4.9990
2.1661
0.0825
-2.0219
23.6787
The output tells us that the regression equation is,
Monthly Profit = 11.6599+10.8284*Monthly Advertising Cost
b. In August, the manager plans to spend $17,000 on
advertising. Based on the data, how much profit should he
expect that month? (Round to the nearest $1000.)

13. c. Given the relationship shown by the paired scores, can you
think of a reason why the manager doesn’t spend a lot more
money on advertising?
18. In Chapter 6, Problem 22 (p. 153), data were presentedfrom
a study conducted to determine the relationshipbetween
religious involvement and self-esteem. Thedata are again
presented below.
Subject ReligiousInvolvement Self-Esteem
1 5 8
2 25 3
3 45 2
4 20 7
5 30 5
6 40 5
7 1 4
8 15 4
9 10 7
10 35 3
a. Assuming a linear relationship, derive the
leastsquaresregression line for predicting self-esteemfrom
religious involvement.
SUMMARY OUTPUT

14. Regression Statistics
Multiple R
0.5626
R Square
0.3165
Adjusted R Square
0.2310
Standard Error
1.7440

15. Observations
10
ANOVA
df
SS
MS
F
Significance F
Regression
1
11.2667
11.2667
3.7041
0.0905

16. Residual
8
24.3333
3.0417
Total
9
35.6000
Coefficients
Standard Error
t Stat
P-value
Lower 95%
Upper 95%
Intercept
6.4885
1.0363
6.2614
0.0002
4.0989
8.8782

17. Religious Involvement
-0.0747
0.0388
-1.9246
0.0905
-0.1642
0.0148
b. Using this regression line, what value of selfesteemwould
you predict for an eighth graderwhose value of religious
involvement is 43?
References
Academic Web Services (n.d.).The Visual Learner –
Statistics.Retrieved from: http://lc.gcumedia.com/hlt362v/the-
visual-learner/quantitative.html.
Pagano, R. (2013). Understanding Statistics in theBehavioral
Sciences (10th ed.). Wadsworth-CengageLearning.
Y-Values 60 75 70 72 54 83 80 65 60 100 80
68 73 97 85 90