Multiple Regression Report
This assignment will help you understand proper reporting and interpretation of
multiple regression. You will use the IBM SPSS Linear Regression procedure to
accurately compute a multiple regression with the Regression Data file given in
the resources. Use the DAA Template given in the resources to write up your
assignment.
Step 1
Write Section 1 of the DAA. Provide a context of the Regression Dataset.
Specifically, imagine that you are a health researcher studying how well a
measure of anxiety ( X1) and weight ( X2) predict systolic blood pressure ( Y) . In
Section 1 of the DAA, articulate your predictor variables, the outcome variable,
and the scales of measurement for each variable. Specify the sample size of the
dataset.
Step 2
Write Section 2 of the DAA. Test the four assumptions of multiple regression.
Begin with SPSS output of the three histograms on X1, X 2, and Y and provide
visual interpretations of normality. Next, paste the SPSS output of the scatterplot
matrix and interpret it in terms of linearity and bivariate outliers. Next, paste
SPSS output of the zero-order correlations (Pearson r) and interpret it to check
the multicollinearity assumption. Note: To test this assumption in SPSS, use
Analyze… Correlate… Bivariate Correlations to generate a two-tailed test; do not
use the default one-tailed test output from the Linear Regression procedure.
Finally, paste the SPSS plot of standardized residuals (ZPRED = x-axis; ZRESID
= y-axis) and interpret it to check the homoscedasticity assumption.
Step 3
Write Section 3 of the DAA. Specify a research question for the overall
regression model. Articulate a null hypothesis and alternative hypothesis for the
overall regression model. Specify a research question for each predictor.
Articulate the null hypothesis and alternative hypothesis for each predictor.
Specify the alpha level.
Step 4
Write Section 4 of the DAA. Begin with a brief statement reviewing assumptions.
Next, paste the SPSS output for the Model Summary. Report R and R2;
interpret R2 effect size. Next, paste the SPSS ANOVA output. Report the F test
for R and interpret it against the null hypothesis. Next, paste the SPSS
Coefficients output. For each predictor, report the b coefficient, the t test results,
including interpretation against the null hypothesis, the semipartial squared
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correlation effect size, and the interpretation of effect size. In your Interpretation
section, following Table 11.1 on page 460 of your Applied Statistics text, generate
a table of results for the Regression Dataset that summarizes:
The means and standard deviations of each variable in the regression equation.
The zero-order (Pearson r) correlations among variables.
The y-intercept.
The b coefficients of each predictor with notation of calculated p-values for rejecting the
null hypothesis.
The β coefficients of each predictor.
The squared semipartial correlations of each predictor.
The values of R, R2, and adjusted R2 with notation of p-values for rejecting the null
hypothesis.
Step 5
Write Section 5 of the DAA. Discuss your conclusions of the multiple regression
as it relates to your stated research questions for the overall regression model
and the individual predictors. Conclude with an analysis of the strengths and
limitations of multiple regression.
DATA ANALYSIS AND APPLICATION
Data Analysis and Application
Cornell Jones
Capella University
1
DATA ANALYSIS AND APPLICATION
2
[Introduction.] Use this file for all assignments that require the DAA Template. Although the
statistical tests will change from week to week, the basic organization and structure of the DAA
remains the same. According to the sixth edition of Publication Manual of the American
Psychological Association, the introduction of a manuscript is clearly identified by its position
within it, and therefore does not have a heading to label it as the introduction. Remove this text
and provide a brief introduction.
Data File Description [one paragraph]
1) Describe the context of the data set. Cite a previous description if the same data set is used
from a previous assignment. To increase the formal tone of the DAA, avoid first-person
perspective “I.” For example, do not write, “I ran a scatter plot shown in Figure 1.” Instead,
write, “Figure 1 shows…” All paragraphs are indented. Your paragraphs will not be numbered as
these are in the template.
2) Specify the variables used in this DAA and the scale of measurement of each variable.
3) Specify sample size (N).
Testing Assumptions [multiple paragraphs]
1) Articulate the assumptions of the statistical test.
2) Paste SPSS output that tests those assumptions and interpret them. Properly embed SPSS
output where appropriate. Do not string all output together at the beginning of the section. In
other words, interpretations of figures and tables should be near (i.e., immediately above or
below) where the output appears. Format figures and tables per APA (6th edition) style and
formatting rules. Refer to the following examples on the next page.
DATA ANALYSIS AND APPLICATION
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Figure 1. Scatter plot of IQ scores and ADDSC scores taken from a Howell (2011) data set.
Figure 1 above shows the negative linear relationship between…
Table 1 below shows the intercorrelations, means, and standard deviations of…
Table 1
Intercorrelations, Means, and Standard Deviations for Scores on IQ, ADDSC, and GPA
______________________________________________________________________________
Measure
1
2
3
M
SD
______________________________________________________________________________
1. IQ
--
2. ADDSC
-.63**
--
3. GPA
.50**
-.62**
--
100.26
12.99
52.60
12.42
2.46
.86
______________________________________________________________________________
Note. Intercorrelations taken from a Howell (2011) data set (N = 88). **p < .01.
DATA ANALYSIS AND APPLICATION
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3) Summarize whether or not the assumptions are met. If assumptions are not met, discuss how
to ameliorate violations of the assumptions.
Research Question, Hypotheses, and Alpha Level [one paragraph]
1) Articulate a research question (or questions) relevant to the statistical test.
2) Articulate the null hypothesis and alternative hypothesis for the research question(s).
3) Specify the alpha level.
Interpretation [multiple paragraphs]
1) Paste SPSS output for an inferential statistic and report it. Properly embed SPSS output where
appropriate. Do not string all output together at the beginning of the section. In other words,
interpretations of figures and tables should be near (i.e., immediately above or below) where the
output appears. Format figures and tables per APA formatting rules.
2) Report the test statistics. Refer to Warner (2013) “Results” examples at the end of the
appropriate chapter for guidance.
3) Interpret statistical results against the null hypothesis.
Conclusion [two paragraphs]
1) Provide a brief summary (i.e., one paragraph) of the DAA conclusions.
2) Analyze strengths and limitations of the statistical test.
DATA ANALYSIS AND APPLICATION
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References
Howell, D. C. (2011). Fundamental statistics for the behavioral sciences. (7th ed.). Belmont,
CA: Wadsworth.
1) Provide references if you include in-text citations. Do not cite Capella course materials (e.g.,
instructor notes, handouts, class announcements, and so on). Only cite primary and secondary
sources (e.g., textbooks and empirical journal articles). Be sure that your reference page remains
on a separate page.
Anxiety
Weight
7
10
35
19
17
11
18
36
19
22
28
25
4
25
18
7
16
25
28
10
34
22
17
16
9
90
130
30
151
170
190
210
91
90
95
130
150
110
150
110
150
230
315
250
210
271
250
230
185
201
SBP
137
158
163
133
106
128
168
145
149
143
145
123
145
143
113
119
139
173
176
178
174
176
156
144
154
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