RCH 8303, Quantitative Data Analysis 1
Course Learning Outcomes for Unit VIII
Upon completion of this unit, students should be able to:
1. Perform statistical tests using software tools.
1.1 Perform general linear regression using appropriate data file and menu options.
2. Explain results of statistical tests.
2.1 Describe the selection process of the variables in the data file.
2.2 Discuss the differences between alternative hypotheses
2.3 Elaborate on options available for missing or incomplete data.
2.4 Describe the assumptions for general linear regression.
2.5 Contrast the differences between association and prediction.
2.6 Describe homoscedasticity.
2.7 Describe dummy-coding and when this would be used in regression.
3. Judge whether null hypotheses should be rejected or maintained.
3.1 Explain the differences between the null and alternative hypotheses, and perform option
selection.
3.2 Explain the difference between R and R².
4. Apply appropriate statistical tests based on given scenarios.
4.1 Explain the differences between the null and alternative hypotheses, and perform option
selection.
4.2 Explain the difference between R and R².
5. Explain differences between parametric and nonparametric statistical tests.
5.1 Describe the process to determine whether data are normally distributed or not.
5.2 Explain the difference between R and R².
Course/Unit
Learning Outcomes
Learning Activity
1.1
Unit Lesson
Chapter 7, pp. 129–170
Unit VIII Assignment 2
2.1, 2.2, 2.3, 2.4, 2.5,
2.6, 2.7
Unit Lesson
Chapter 7, pp. 129–170
Unit VIII Assignment 1
3.1, 3.2, 4.1, 4.2, 5.1,
5.2
Unit Lesson
Chapter 7, pp. 129–170
Unit VIII Assignment 1
Unit VIII Assignment 2
Required Unit Resources
Chapter 7: Fitting Linear and Generalized Linear Models, pp. 129–170
UNIT VIII STUDY GUIDE
Regression, Generalized
Linear Models
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Unit Lesson
Unit VIII Plan
The Unit VIII assignment will be in two parts. Part 1 of your assignment requires you to complete one module
of the CITI Program EOSA that relates directly to the reading in this unit. The module has a final quiz that
must be completed and successfully passed, demonstrating your knowledge of basic statistics and the
research process.
For Part 2, you will review how to conduct a multiple regression, and determine whether the test is statistically
significant or not.
The topic of the Unit VIII CITI EOSA course is below.
Multiple Regression (ID 17635): This module describes and explains how multiple predictors explain variance
in an outcome variable. The module describes how to evaluate the significance of a model as a whole and of
a new block of predictors. The module discusses the rule of thumb that at least 10 cases in the sample are
needed for every predictor variable. The assumptions of multiple regression and what to do if the data violates
one or more of the assumptions is discussed. In addition, multicollinearity is introduced as an assumption for
multiple regression.
Unit VIII Lesson
Unit VIII continues with regression, which is a methodology that allows the researcher to use multiple
predictor (independent) variables to explain variability in the researcher’s outcome (dependent) variable. As
noted in Unit VII, an example of this could be whether the researcher could explain the variability in the
outcome variable cancer using the predictor variable smoking? Can smoking be a predictor of cancer? A
researcher could gather data on whether smoking could or would predict cancer in a sample of smokers.
Multiple regression adds another ability to the researcher’s toolkit. Instead of only using one independent
variable (predictor) as was done in Unit VII, multiple regression allows us to use many more. The multiple
regression module notes that the primary goal of multiple regression is to explain as much variability in
outcome variables as possible. Note the plural on outcome variables. This means we have more than one
predictor variable.
R and R Commander make it very easy to conduct simple statistical tests.
As noted in Unit III, once data are collected, a researcher needs to be able to describe, summarize, and,
potentially, detect patterns in the data they have recorded with meaningful numerical scales such as
histograms. After reviewing the data, decisions must be made regarding whether the assumptions of the
particular test have been met. If they have, then conducting of the test can proceed. Reviewing these two
tutorials, Homogeneity of Variances and Testing for Normality, will be very helpful to you.
Prior to conducting any statistical test though, the researcher must first meet the assumptions of the particular
test. The Multiple Regression (ID 17635) module describes and explains each of the assumptions for
regression.
For an example of multiple regression, make sure when you access R that you also load R Commander. Type
in library(Rcmdr) or see Unit I for a refresher on how to gain access to R Commander. Once R and R
Commander have been loaded, the next step is to load the data set wtandruntimeandheight that will be used
(Figure 1).
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Figure 1
Data Set Wtandruntimeandheight Successfully Uploaded
“
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Viewing the data set allows a user to examine the type of category information and numeric values (Figure 2).
Figure 2
Visual Representation of Wtandruntimeandheight Data Set
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In this test, our research question and hypotheses could be written as:
RQ: The purpose of this study was to examine the variables height and weight and determine its
relationship to runtimes.
H0: There is no relationship between height and weight and runtimes.
HA: There is a relationship between height and weight and runtimes.
The first step is to run the multiple regression to determine whether our weight and height predictor
(independent) variables explain variability in the researcher’s runtimes outcome (dependent) variable (Figure
3).
Figure 3
Linear Regression Selection Menu
Our next step is to select which variable is our dependent variable (or as R calls this, Response variable) and
which variable is our Explanatory variable. Page 129 of our textbook explains the terms used as the
dependent and independent variables. In our case, our dependent variable (Response variable) is runtimes
and our independent variables (Explanatory variables) are Height and Weight (Figure 4).
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Figure 4
Variable Selection Menu
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Once “OK” is pressed, the multiple regression output display is shown (Figure 5).
Figure 5
Multiple Regression Test Output Display
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Next, examine the regression diagnostics to address the hypotheses (Figure 6).
Figure 6
Regression Diagnostics Menu Option
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Once “OK” is selected, the diagnostic graphs are shown (Figure 7).
Figure 7
Regression Diagnostic Output
Pages 163–170 of the textbook discuss various options applicable to your specific test.
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The results of this test could be written as:
A multiple regression analysis was performed to examine the predictive strength that a person’s
weight and height have on a person’s runtime. The results of the test are significant, F (2, 17) =
26.13, p < .001, R2 = .755, Adj R2 = .726. A person’s weight and height accounts for 73% of the
variance in their runtimes.
In conclusion, the multiple regression test discussed in this unit has asked the following question; Can I
predict which variable has the most effect on the dependent variable? Or, to ask another way, Can runtimes
be predicted with height and weight scores?
Learning Activities (Nongraded)
Nongraded Learning Activities are provided to aid students in their course of study. You do not have to submit
them. If you have questions, contact your instructor for further guidance and information.
When studying APA formatting, pay particular attention to the sections that pertain to formatting for research
and statistics. Review these sections as needed.
