Unit VII discussion Board RCH

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Course Learning Outcomes for Unit VII Upon completion of this unit, students should be able to:

1. Perform statistical tests using software tools. 1.1 Perform simple 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 simple 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.

Course/Unit Learning Outcomes

Learning Activity

1.1 Unit Lesson Chapter 7, pp 129–144 Unit VII Assignment 2

2.1, 2.2, 2.3, 2.4, 2.5, 2.6, 2.7

Unit Lesson Unit VII Assignment 1

3.1, 3.2 Unit Lesson Unit VII Assignment 2

Required Unit Resources Chapter 7: Fitting Linear and Generalized Linear Models, pp. 129–144

Unit Lesson

Unit VII Plan The Unit VII 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 this readings 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 simple linear regression and determine whether the test is statistically significant or not. There is one topic for the Unit VII CITI EOSA course. Simple Linear Regression (ID 17634): This module describes and explains differences among association, prediction, and causality. The module describes the assumptions of linear regression and what to do if the

UNIT VII STUDY GUIDE

Simple Linear Regression

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data violate one or more of the assumptions. The module also displays how to enter continuous, dichotomous, and categorical predictors into a regression model.

Unit VII Lesson Unit VII starts on a different type of outcome form of testing. Units IV, V, and VI conducted tests that compared the means, and in some cases, causation or a relationship could be determined. The focus of Unit VII is 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. An example of this could be whether the researcher could explain the variability in the outcome variable cancer using the predictor variable “smoking”? Another way of looking at this could be, “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. 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. Tutorials are provided in the Dissertation Center for this lesson. Reviewing the Testing for Normality will be very helpful to you. Before conducting any statistical test, though, the researcher must first meet the assumptions of the particular test. The Simple Linear Regression (ID 17634) module describes and explains each of the assumptions for regression. For an example of simple linear 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 wtandruntimes1 that will be used (Figure 1).

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Figure 1 Data Set Wtandruntimes1 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 Wtandruntimes1 Data Set

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In this test, our research question and hypotheses could be written as:

RQ: Does a person’s weight predict their runtime? H0: A person’s weight does not predict their runtime. HA: A person’s weight predicts their runtime.

The first step is to view a scatterplot. In a scatterplot, one variable is plotted on the x-axis and the other variable is plotted on the y-axis. Select Graphs and Scatterplot (Figure 3). Figure 3 Scatterplot selection menu

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Once the menu item is selected, place Weight variable in the x-axis and the runtimes variable in the y-axis (Figure 4). Figure 4 Scatterplot Variable Selection Menu

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Press “OK,” and view the scatterplot in the output window (Figure 5). Figure 5 Scatterplot Results

Note the scatterplot illustrates a positive (upward) line with six data points results not on the regression line.

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Our next step is to run the linear regression to determine whether our Weight predictor (independent) variable to explain variability in the researcher’s runtimes outcome (dependent) variable (Figure 6). Figure 6 Linear Regression Selection Menu

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Once linear regression is selected, you must place the Weight and runtimes variable into the appropriate Explanatory or Response position. Fox (2017) explains the terms used as the dependent and independent variables on page 129. In our case, our dependent variable (Response variable) is runtimes, and our independent variable (Explanatory variable) is Weight (Figure 7). Figure 7 Variable Selection Menu ""

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Once “OK” is pressed, the results of the simple linear regression is displayed in the output window (Figure 8). Figure 8 Simple Linear Regression Test Output Display ""

Note that from the output, the model is significant (p < .001), and that 72.7% of the change in runtimes can be attributed to a person’s weight.

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Next, you must examine the regression diagnostics to address the assumptions of the test (Figure 9). Figure 9 Regression Diagnostics Menu Option

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Once “OK” is selected, the diagnostic graphs are the output (Figure 10). Figure 10 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 simple regression analysis was performed to examine whether a person’s weight predicts their runtime. The results of the test was significant, F(1,18) = 47.91, p < .001, R2 = .727. This can be interpreted as 73% of the change in runtime is attributable to a person’s weight.

In conclusion, the simple regression test discussed in this unit has asked the question; Can I predict which variable has the most effect on the dependent variable? Or, put another way; Can runtimes be predicted with weight scores? Our final unit, Unit VIII, will expand on regression. However, instead of only having one predictor variable (independent variable), Unit VIII focuses on multiple regression and the researcher can have many independent variables. In Unit VIII, we will be asking the following question; Can I predict which variable(s) has the most effect on the dependent variable? Or put another way, Can runtimes be predicted with multiple variables?

Reference Fox, J. (2017). Using the R Commander: A point-and-click interface for R. CRC Press.

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.