NORTHCENTRAL

UNIVERSITY

ASSIGNMENT

COVER SHEET

Student:

Scott Leonard Burgess

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EDR8201

Dr. Watts

Statistics I

Week 6 – Assignment:

Analyze Correlation and Regression

Faculty

Use Only

Week 6—Assignment: Analyze

Correlation and Regression (10 Points)

Download the

EDR-8201 Week 6 Worksheet found in this week’s resources and use it to complete

this assignment.

Imagine a researcher is interested in examining the

relationship of self-esteem (ScoreOne) and productivity (ProdOne). The

researcher is also interested in the ability to predict the productivity of

teachers using years of teaching (Experience) as the predicting variable. Use

the “teachersurvey.sav” data set to conduct the analysis involving ScoreOne,

ProdOne, and Experience. Use these data to answer the questions below (these

data have already been entered into the “teachersurvey.sav” SPSS file).

Gender

(M=male, F= female)

Self-esteem scores

ScoreOne

How long have you been teaching (in years)? Experience

Productivity scores

ProdOne

M

64

25

25

M

68

14

28

F

74

10

36

M

75

20

38

F

76

30

34

F

79

2

36

F

80

23

40

F

82

13

41

M

68

29

22

M

70

19

38

F

74

22

39

F

76

5

34

F

78

16

38

F

79

11

37

M

82

15

45

M

85

2

46

F

71

15

30

M

73

11

34

F

75

18

33

M

77

10

36

M

78

21

38

M

80

5

42

F

83

18

46

F

86

21

49

M

73

17

37

F

74

15

38

M

77

18

32

M

77

12

35

F

78

8

36

M

81

3

45

F

84

33

49

F

87

16

48

F

77

29

36

M

71

19

33

F

75

4

34

F

76

17

36

M

79

30

38

M

83

20

48

F

89

11

48

F

91

14

49

NOTE: Not all of the

variables in the “teachersurvey.sav” file will be used for this assignment.

In this SPSS assignment, you will expand your understanding

of inferential statistics involving correlation and regression. Complete the

following:

1.

Produce an SPSS analysis for a correlation between

participants’ self-esteem and productivity.

Descriptive Statistics

Mean

Std. Deviation

N

ScoreOne

77.63

5.808

40

ProdOne

38.18

6.586

40

Correlations

ScoreOne

ProdOne

ScoreOne

Pearson Correlation

1

.897**

Sig. (2-tailed)

.000

N

40

40

ProdOne

Pearson Correlation

.897**

1

Sig. (2-tailed)

.000

N

40

40

**. Correlation is

significant at the 0.01 level (2-tailed).

Correlations

1=male, 2=female

ProdOne

ScoreOne

1=male, 2=female

Pearson Correlation

1

.210

.318*

Sig. (2-tailed)

.194

.046

N

40

40

40

ProdOne

Pearson Correlation

.210

1

.897**

Sig. (2-tailed)

.194

.000

N

40

40

40

ScoreOne

Pearson Correlation

.318*

.897**

1

Sig. (2-tailed)

.046

.000

N

40

40

40

*. Correlation is

significant at the 0.05 level (2-tailed).

**. Correlation is

significant at the 0.01 level (2-tailed).

a. Provide the null and alternative

hypotheses.

Ho: There will be a non-significant relationship

in existence between the self-esteem of the participants and productivity

scores of the participants.

Ha: There will be a significant relationship in

existence between self-esteem of the participants and productivity scores of

the participants.

b. Determine if a Pearson correlation or

Spearman correlation will be used, and explain why. Explain the condition when

it is appropriate to use the other test.

The Pearson correlation will be used because the variables

within the data are considered interval or ratio scales. If the variables in

the data set included ordinal scales then the Spearman correlation would be

used, but that is not the case since the variables are continuous variables.

Therefore, the Pearson correlation needs to be used rather than the Spearman

correlation with the ranked data.

c. What is the effect size? Explain whether it

is small, medium, or large.

When observing the effect size

within the correlation will be r2 or (.897)2 = .805.

Therefore, observing there is an indication that the self-esteem along with the

productivity scores have a variance of 80% commonality. This would then make

the effect size large.

d. Report the results in APA format.

The Pearson correlation coefficient test was conducted which

assessed the relationship amongst the self-esteem and productivity of the

participants. The evidence supported that r = .897 and p = .000 (p < .01).
The Pearson correlation coefficient test results are an indicator for a
significant, positive correlation amongst the self-esteem and productivity of
the participants.
e. What conclusions can be made?
When conducting an analysis of the data the null hypothesis
is rejected while there is an acceptance of the alternative hypothesis. The
Pearson correlation coefficient test results are an indicator for a
significant, positive correlation amongst the self-esteem and productivity of
the participants. Therefore, the null hypothesis is rejected based on the
conducted analysis of the data set.
2. Produce an SPSS analysis using regression
to examine the impact of participants' years of experience on their productivity.
Descriptive Statistics
Mean
Std. Deviation
N
ProdOne
38.18
6.586
40
Experience
16.03
7.995
40
Correlations
ProdOne
Experience
Pearson Correlation
ProdOne
1.000
-.116
Experience
-.116
1.000
Sig. (1-tailed)
ProdOne
.
.237
Experience
.237
.
N
ProdOne
40
40
Experience
40
40
Model Summary
Model
R
R Square
Adjusted R Square
Std. Error of the Estimate
Change Statistics
R Square Change
F Change
df1
df2
Sig. F Change
1
.116a
.014
-.012
6.627
.014
.522
1
38
.474
a. Predictors: (Constant),
Experience
ANOVAa
Model
Sum of Squares
df
Mean Square
F
Sig.
1
Regression
22.946
1
22.946
.522
.474b
Residual
1668.829
38
43.917
Total
1691.775
39
a. Dependent Variable:
ProdOne
b. Predictors: (Constant),
Experience
Coefficientsa
Model
Unstandardized Coefficients
Standardized Coefficients
t
Sig.
95.0% Confidence Interval for B
B
Std. Error
Beta
Lower Bound
Upper Bound
1
(Constant)
39.712
2.371
16.749
.000
34.913
44.512
Experience
-.096
.133
-.116
-.723
.474
-.365
.173
a. Dependent Variable:
ProdOne
a. Provide the null and alternative
hypotheses.
Ho: There will be a non-significant influence
within the participants productivity and for the participants years of
experience.
Ha: There will be significant influence for the participants
productivity and the participants years of experience.
b. What is the effect size? Explain whether it
is small, medium, or large.
When observing the effect size
within the correlation will be r2 or (.116) 2 = .014. Therefore, the effect size would be
resulting a small effect size.
c. Report the results in APA format.
There was a simple regression completed to analyze if there
was any influence based on the years of experience for the participants and the
productivity of the participants. When observing the results, the results
indicated how the participants productivity did not significantly influence the
participants years of experience. As was shown, R = .116, F(1, 39) = .522, and
p = .474 (p > .05). Therefore, there the results fail to reject the null

hypotheses.

d.

What can be

concluded from these results? Be sure to consider possible study limitations

and provide recommendations for future research.

The years of

experience the participants had does not significantly influence the

productivity of the participants. Based on the limitations within the study

there is that there was simple linear regression model being utilized. A

recommendation for the study would be to use a multilinear regression model and

include interaction. If the study was based on a multilinear regression model

the study would most likely have a change in the conclusion.

e. Given only two variables were examined, how

does testing the significance of the regression equation relate to testing the

significance of the Pearson correlation?

When given only two variables being examined the testing of

the significance regression equation relates to testing the significance of the

Pearson correlation because when conducting a regression analysis, a predictive

relationship is being established with the variables. While with the

correlation analysis, there is a linear relationship being established with the

variables. Therefore, with the predictive relationship there are patterns or

predication which can be made for the outcomes, while the linear relationship

the opposite is not going be necessarily true because prediction sometime

cannot be made and there may be a corresponding change occurring.

3. Based on your personal experiences and

interests, briefly discuss two variables to be used in a correlational analysis

and two variables to be used in a regression analysis.

Based on my personal experience with being an educator, the

two variables that would be used for a correlational analysis would be to

explore if a relationship exists between assessments (test taking) and the

increase in anxiety when students are being assessed. Likewise, the two

variables which could be used within the regression analysis are the sleeping

patterns for the students with anxiety and the influence of the class

performance or the ability to learn.

References

Bar-Gera, H. (2017). The target parameter of adjusted

R-squared in fixed-design experiments. American Statistician, 71(2),

112-119. doi:10.1080/00031305.2016.1200489

Fowokan, A. O., Lesser, I. A., Humphries, K. H., Mancini,

J. G. B., & Lear, S. A. (2017). The predictive relationship between

baseline insulin and glucose with subclinical carotid atherosclerosis after 5

years in a multi-ethnic cohort. Atherosclerosis, 257, 146-151.

doi:10.1016/j.atherosclerosis.2016.12.013

Garcia-Arroyo, J., & Osca, A. (2017). Coping

with burnout: Analysis of linear, non-linear and interaction relationships Retrieved

from http://proxy1.ncu.edu/login?url=http://search.ebscohost.com.proxy1.ncu.edu/login.aspx?direct=true=edswss=000406566500031=eds-live

Knapp, H. (Academic). (2017). Correlation and

regression—Pearson Video file. London: SAGE Publications Ltd.

Miles, J. (2011). Regression analysis. In N. J. Salkind

(Ed.), Encyclopedia of measurement and statistics (pp. 830-832). Thousand Oaks,

CA: SAGE Publication

Vogt, W.P. (2011).

Pearson’s correlation coefficient. (Ed.), Dictionary of statistics &

methodology (pp. 233-234). Thousand Oaks, CA: SAGE Publication

Waterman, R. (Academic). (2014). Correlation & simple

regression Video file. Philadelphia, PA: SAGE Publications Ltd.