BIVARIATE REGRESSION
Write Up: Bivariate Regression
Andrea Williams
School of Education, Liberty University
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BIVARIATE REGRESSION 2
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Instructions: For this graded assignment, you will complete the write-up below after completing
the corresponding tutorial to this assignment. You will delete figures and tables where
appropriate and then insert correct figures and tables. Also delete and then insert correct answers
where there is RED text
Scenario: The purpose of this study was to see if the number of nurses employed at a hospital
could predict patient satisfaction. Researchers examined 20 hospitals similar in size and location.
The amount of nurses working full-time for the hospitals were gathered from HR and patient
satisfaction was averaged from surveys gathered over the past year. The patient satisfaction
survey ranges from 1 to 10 with 1 being not satisfied and 10 being extremely satisfied.
To begin, select the “Data View” tab, then cut and paste the data set below into SPSS (or you can
type in the data manually). Do not copy the header row when you paste into SPSS.
CodeNumber ofPatient
Nurses Satisfaction
1 200 7.1
2 187 6.3
3 254 8.8
4 210 7.3
5 200 6.9
6 190 6.2
7 160 5.4
8 214 7.8
9 198 6.6
10 186 6.4
11 270 9.1
12 215 7.0
13 175 5.6
14 300 9.3
152508.1
16 155 5.0
17 198 7.0
18 212 7.4
19 215 7.2
20 195 6.9
W -U: B R T
RITE IVARIATE EGRESSION EMPLATE
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BIVARIATE REGRESSION3
FINDINGS
Overview
The purpose of this study was to see if the number of nurses employed could predict
patient satisfaction. The independent variable was the number of nurses employed. The
dependent variable was patient satisfaction. A bivariate regression was used to test the
hypothesis. The Findings section includes the research question, null hypothesis, data screening,
descriptive statistics, assumption testing, and results.
Research Question
RQ: Is there a significant predictive relationship between the dependent variable (patient
satisfaction) and the independent variable (number of nurses employed) for a group of similar
hospitals.
Null Hypothesis
H0: There is no significant relationship between the dependent variable (patient
satisfaction) and the independent variable (number of nurses employed) for a group of similar
hospitals.
Data Screening
The researcher sorted the data and scanned for inconsistencies on each variable. No data
errors or inconsistencies were identified. A scatter plot was used to detect bivariate outliers
between the independent variable and the dependent variable. No bivariate outliers where
identified. See Figure 1 for the scatter plots.
BIVARIATE REGRESSION
Figure 1
Simple Scatter Plot
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Descriptive Statistics
Descriptive statistics were obtained on each of the variables. The sample consisted of 20
participants. The number of nurses at each hospital was obtained through HR. Patient satisfaction
scores were obtained through averaging surveys obtained throughout the past year. Patient
satisfaction scores could range from 1 (not satisfied at all) to 10 (extremely satisfied).
Descriptive statistics can be found in Table 1.
Nurses
Satisfaction
Valid N (listwise)
Table 1
Descriptive Statistics
N
2
0
2
0
2
0
BIVARIATE REGRESSION
Minimum
155
5
Maximum
300
9
Mean
209.20
7.07
Std. Deviation
35.734
1.151
Assumption of Bivariate Normal Distribution
The bivariate regression requires that the assumption of bivariate normal distribution be
met. The assumption of bivariate normal distribution was examined using a scatter plot. The
assumption of bivariate normal distribution was met. See Figure 1 for scatter plot.
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Assumption Testing
Assumption of Linearity
The multiple regression requires that the assumption of linearity be met. Linearity was
examined using a scatter plot. The assumption of linearity was met. See Figure 1 for the bivariate
scatter plot.
Table 3
Regression Model
ModelSum of Squares 1 Regression
23.441
Residual 1.741
Total 25.182
a. Dependent Variable: Satisfaction
b. Predictors: (Constant), Nurses
df
1
1
8
1
9
Mean Square
23.441
.097
F
242.293
BIVARIATE REGRESSION6
Results
A bivariate regression was conducted to see if the number of nurses employed at a
hospital could predict patient satisfaction. The independent variable was the number of nurses
employed. The dependent variable was patient satisfaction scores. The researcher rejected the
null hypothesis at the 95% confidence level where F(1, 18) = 242.29, p <.001. There was a
statistical relationship between the independent variable (SAT exam scores) and the dependent
variable Praxis 1 exam score). See Table 3 for regression model results.
The model’s effect size was extremely large where R = .965. Furthermore, R2 = .931
indicating that approximately 93.1% of the variance of dependent variable can be explained by
the independent variable. See Table 5 for model summary.
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Sig.
.000
b
BIVARIATE REGRESSION
Table 5
Model Summary
Model Summary
ModelRR Square
1 .965a .931
a. Predictors: (Constant), Nurses
Adjusted R Square
.927
Std. Error of the
Estimate
.311
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