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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.