Solved by verified expert:Multiple RegressionMultiple linear regression is a logical extension to the Pearson Product-Moment Correlation test. Researchers use multiple linear regression to examine the relationship between at least two predictor variables and a scale (numerical) dependent variable. Multiple linear regression is the most commonly used statistical test for quantitative DBA studies.For this Assignment, you will run a multiple linear regression using the Week 6 Data File for Multiple Linear Regression. You will use “job satisfaction” as the dependent variable.To prepare for this Assignment, review Lesson 16A and Lessons 31–35 in your Green and Salkind (2017) text, the Week 6 Assignment Exemplar and Week 6 Assignment Template documents, as well as the tutorial videos provided in this week’s Resources. Consider how a multiple regression analysis will allow you to answer your research questions effectively.By Day 7Submit a synthesis of statistical findings derived from multiple regression analysis that follows the Week 6 Assignment Template. Your synthesis must include the following:An APA Results section for the multiple regression test [see an example in Lesson 34 of the Green and Salkind (2017) text].Only the critical elements of your SPSS output:A properly formatted research questionA properly formatted H10 (null) and H1a (alternate) hypothesisA descriptive statistics narrative and properly formatted descriptive statistics tableA properly formatted scatterplot graphA properly formatted inferential APA Results Section to include a properly formatted Normal Probability Plot (P-P) of the Regression Standardized Residual and the scatterplot of the standardized residualsAn Appendix including the SPSS output generated for descriptive and inferential statisticsAn explanation of the differences and similarities of bivariate regression analysis and multiple regression analysesNote: You will cut and paste the appropriate SPSS output into the Appendix. The SPSS output is not in APA format, so you will need to type the information from the SPSS output to the appropriate sections of the APA table. You must use the Week 6 Assignment Template to complete this Assignment. Also, refer to the Week 6 Assignment Rubric for specific grading elements and criteria. Your Instructor will use this rubric to assess your work.
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DDBA 8307 Week 6 Assignment Exemplar – Multiple Regression
John Doe
DDBA 8307-6
Dr. Jane Doe
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Multiple Linear Regression
Type text here. Describe and defend using the multiple linear regression test for
your analysis. Use at least two outside resources—that is, resources not provided in the
course resources, readings, etc. These citations will be presented in the References
section. This exercise will give you practice for addressing Rubric Item 2.13b, which
states, “Describes and defends, in detail, the statistical analyses that the student will
conduct….” This section should be no more than two paragraphs.
Research Question
Is there a statistically significant relationship between stress, engagement, intent
to leave, and job satisfaction?
Hypotheses
H0: There is not a statistically significant relationship between stress, engagement,
intent to leave, and job satisfaction.
H1: There is a statistically significant relationship between stress, engagement,
intent to leave, and job satisfaction.
Results
In this subheading, I will present descriptive statistics, discuss testing of the
assumptions, present inferential statistic results, and conclude with a concise summary.
Descriptive Statistics
A total of 426 employees participated in the study. The assumptions of outliers,
multicollinearity, normality, linearity, homoscedasticity, and independence of residuals
were evaluated with no significant violations noted. Table 1 depicts descriptive statistics
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for the study variables. Figure 1 depicts a scatter plot of the bivariate correlation,
indicative of a negative linear relationship between job satisfaction and intent to leave.
Table 1
Means and Standard Deviations for Quantitative Study Variables
M
SD
Bootstrapped 95% CI (M)1
Stress
26.36
10.56
[24.80, 27.94]
Engagement
43.60
12.51
[41.90, 45.28]
Intent to leave
72.34
15.21
[70.23, 74.51]
Job satisfaction
169.12
10.00
[167.68, 170.44]
Variable
Note: N = 204.
Descriptive Statistics for Study Variables
Variable
M
SD
Stress
Engagement
Intent to leave
Job satisfaction
Tests of Assumptions
The assumptions of multicollinearity, outliers, normality, linearity,
homoscedasticity, and independence of residuals were evaluated. Bootstrapping, using
1,000 samples, enabled combating the influence of assumption violations.
Multicollinearity. Multicollinearity was evaluated by viewing the correlation
coefficients among the predictor variables. All bivariate correlations were small to
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The 95% Bootstrap confidence intervals are produced when the bootstrapping procedure is
selected in the SPSS regression process. See the Multiple Linear Regression videos in the Week 6 Learning
Resources.
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medium (Table 2); therefore, the violation of the assumption of multicollinearity was not
evident. The following table contains the correlation coefficients.
Table 2
Correlation Coefficients Among Study Predictor Variables
Variable
Stress
Engagement
Intent to Leave
stress
1.00
.151
-.010
Engagement
.151
1.00
.562
Intent to leave
-.010
.562
1.00
Note. N = 204.
Outliers, normality, linearity, homoscedasticity, and independence of
residuals. Outliers, normality, linearity, homoscedasticity, and independence of residuals
were evaluated by examining the Normal Probability Plot (P-P) of the Regression
Standardized Residual (Figure 1) and the scatterplot of the standardized residuals (Figure
2)2. The examinations indicated there were no major violations of these assumptions. The
tendency of the points to lie in a reasonably straight line (Figure 1), diagonal from the
bottom left to the top right, provides supportive evidence the assumption of normality has
not been grossly violated (Pallant, 2010)3. The lack of a clear or systematic pattern in the
scatterplot of the standardized residuals (Figure 2) supports the tenability of the
assumptions being met. However, 1,000 bootstrapping samples were computed to combat
any possible influence of assumption violations and 95% confidence intervals based upon
the bootstrap samples are reported where appropriate.
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You will run these plots when running the regression procedure.
It is important to note the results of your assumption test will differ from this hypothetical example.
Therefore, you must report the results appropriately for your analysis. Do not copy this example
verbatim; ensure you understand “your” analysis output.
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Figure 1. Normal probability plot (P-P) of the regression standardized residuals.
Figure 2. Scatterplot of the standardized residuals.
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Inferential Results
Standard multiple linear regression4, α = .05 (two-tailed), was used to examine the
efficacy of stress, engagement, and intent to leave in predicting job satisfaction. The
independent variables were stress, engagement, and intent to leave5. The dependent
variable was job satisfaction6. The null hypothesis was that there is not a statistically
significant relationship between stress, engagement, and intent to leave. The alternative
hypothesis was that there is a statistically significant relationship between stress,
engagement, and intent to leave. Preliminary analyses were conducted to assess whether
the assumptions7 of multicollinearity, outliers, normality, linearity, homoscedasticity, and
independence of residuals were met; no serious violations were noted (see Tests of
Assumptions). The model as a whole8 was able to significantly predict job satisfaction:
F(3, 200) = 4.778, p < .003, R2 = .067. The R2 (.067) value indicated that approximately
7% of variations in job satisfaction is accounted for by the linear combination of the
predictor variables (stress, engagement, and intent to leave). In the final model, stress and
intent to leave were statistically significant with stress (t = –3.892, p < .01, β = –.393)
accounting for a higher contribution to the model than intent to leave (t = –2.595, p < .05,
β = –.268). Engagement did not explain any significant variation in job satisfaction. The
final predictive equation was:
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Identify the test and of purpose of the test.
Restate the independent variables as presented in the purpose statement and research question; there
is to be no deviation.
6 Restate the dependent variables as presented in the purpose statement and research question; there is
to be no deviation.
7 Identify the assumptions and state how they were assessed.
8 State whether the model (app predictors included) could predict (or not) the dependent variable. Report
the appropriate statistics (e.g., F(3, 200) = 4.778, p < .003, R2 = .067).
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Job satisfaction = 70.205 – .148(stress) + .109(engagement) – 2.303(intent to leave).
Stress. The negative slope for age (–.148) as a predictor of job satisfaction
indicated there was about a .148 decrease in job satisfaction for each 1-point increase in
stress. In other words, job satisfaction tends to decrease as stress increases. The squared
semi-partial coefficient (sr2) that estimated how much variance in job satisfaction was
uniquely predictable from stress was .03, indicating that 3% of the variance in job
satisfaction is uniquely accounted for by stress, when organizational commitment and
engagement are controlled.
Intent to leave. The negative slope for intent to leave (–2.303) as a predictor of
job satisfaction indicated there was a 2.303 decrease in job satisfaction for each
additional 1-unit increase in intent to leave, controlling for stress and engagement. In
other words, job satisfaction tends to decrease as intent to leave increases. The squared
semi-partial coefficient (sr2)9 that estimated how much variance in job satisfaction was
uniquely predictable from intent to leave was .04, indicating that 4% of the variance in
job satisfaction is uniquely accounted for by intent to leave, when stress and engagement
are controlled. The following table depicts the regression summary.
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Derived from the SPSS output.
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Table 3
Regression Analysis Summary for Predictor Variables
Variable
Stress
Engagement
Intent to leave
Β
10
SE Β
β
11
t
12
13
p
-3.892 <. 01
B 95%14
Bootstrap CI
-.148
0.054
-.393
[-.262, -.025]
.109
3.770
-.038
0.371
.712
[-.008, .245]
-2.303
.888
-.268
-2.595
.011
[-.442, -.081]
Note. N= 204.
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Β values are to be used in the regression equation. These are the unstandardized coefficients in the
SPSS output.
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The beta weights identify which variables contribute more to the model. These are the standardized
coefficients in the SPSS output.
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The test statistic for the hypothesis test for the slope (Β) is derived from the SPSS output and is used to
evaluate the significance of the Β weights, where p ≤ .05 is significant.
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The sig. (p) value for the hypothesis test for the slope (Β); derived from the SPSS output; used to
evaluate the significance of the Β weights, where p ≤ .05 is significant.
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The 95% Bootstrap confidence intervals are produced when the bootstrapping procedure is selected in
the SPSS regression process. See the Multiple Linear Regression videos in the Week 6 Learning Resources.
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References
Type references here in proper APA format.
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Appendix – Multiple Linear Regression SPSS Output
Insert the appropriate SPSS output here.
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DDBA 8307 Week 6 Assignment Template – Multiple Regression
John Doe
DDBA 8307-6
Dr. Jane Doe
2
Multiple Linear Regression
Type text here. Describe and defend using the multiple linear regression test for
your analysis. Use at least two outside resources—that is, resources not provided in the
course resources, readings, etc. These citations will be presented in the References
section. This exercise will give you practice for addressing Rubric Item 2.13b, which
states, “Describes and defends, in detail, the statistical analyses that the student will
conduct….” This section should be no more than two paragraphs.
Research Question
Type research question here.
Hypotheses
H0: Type null hypothesis here.
H1: Type alternative hypothesis here.
Results
In this subheading, I will present descriptive statistics, discuss testing of the
assumptions, present inferential statistic results, and conclude with a concise summary.
Descriptive Statistics
Present appropriate descriptive statistics here.
Tests of Assumptions
Type text here.
Inferential Results
Present appropriate inferential results here.
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References
Type references here in proper APA format.
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Appendix – Multiple Linear Regression SPSS Output
...
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