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Assignment: Testing for Multiple Regression
In Week 9, you completed your Part 1 for this Assignment. For this week, you will complete Part 2 where you will create a research question that can be answered through multiple regression using dummy variables.
Part 2
To prepare for this Part 2 of your Assignment:
• Review Warner’s Chapter 12 and Chapter 2 of the Wagner course text and the media program found in this week’s Learning Resources and consider the use of dummy variables.
• Using the SPSS software, open the Afrobarometer dataset or the High School Longitudinal Study dataset (whichever you choose) found in this week’s Learning Resources.
• Consider the following:
o Create a research question with metric variables and one variable that requires dummy coding. Estimate the model and report results. Note: You are expected to perform regression diagnostics and report that as well.
• Once you perform your analysis, review Chapter 11 of the Wagner text to understand how to copy and paste your output into your Word document.
For this Part 2 Assignment:
Write a 2- to 3-page analysis of your multiple regression using dummy variables results for each research question. In your analysis, display the data for the output. Based on your results, provide an explanation of what the implications of social change might be (Please answer this question).Use proper APA format, citations, and referencing for your analysis, research question, and display of output.
Frankfort-Nachmias, C., & Leon-Guerrero, A. (2018). Social statistics for a diverse society (8th ed.). Thousand Oaks, CA: Sage Publications.
• Chapter 12, “Regression and Correlation†(pp. 325-371) (previously read in Week 8)
Wagner, W. E. (2016). Using IBM® SPSS® statistics for research methods and social science statistics (6th ed.). Thousand Oaks, CA: Sage Publications.
Chapter 11, “Editing Output†(previously read in Week 2, 3, 4, 5. 6, 7, and 8)
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| Subject | Psychology | Pages | 7 | Style | APA |
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Answer
Multiple Regression Using Dummy Variables
A dummy variable refers to an artificial variable formulated to represent an attribute with two or more levels (Cohen, West, & Aiken, 2014). In regression analysis, variable measurement is one of the most significant assumption and in this respect, only numerical variables (interval or ratio scale variables) whose values are directly comparable, are included in the model as independent variables. However, oftentimes, a need arises to include nominal scale variables in the model, and the variables lack relational characteristics represented in a dataset with numbers that only distinguish the levels of variation and do not have intrinsical meaning by themselves. The use of dummy variables solves this intricate need by enabling introduction of dichotomous or binary codes (0s and 1s) to transform the dataset so as to accommodate these non-numerical variables as independent variables in the model (Frankfort-Nachmias & Leon-Guerrero, 2017). This paper reports on the use of dummy variable of number hours spent watching movie or TV on typical school day on mathematics utility.
Dummy Variable in Estimating Mathematics Utility
It has been shown by past research that students who spend more time practicing Mathematics tend to have higher utility of the subject, which has been cited to be difficult for most students (Passolunghi et al, 2016). Therefore, it is hypothesized in this paper that watching more TV and movies will negatively affect Mathematics utility, basing on the supposition that the hours spent watching TV and movies on a typical school day eat up the time that would have been spent revising Mathematics. The research question to be answered in this study is: Does watching more TV and movies on a typical school day affect student’s Mathematics efficacy model when all other factors remain constant?
This study examines the level of linear relationship in the model by adding “hours spent watching television or movies on typical schoolday” as the dummy variable.
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Model Summary |
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Model |
R |
R Square |
Adjusted R Square |
Std. Error of the Estimate |
Change Statistics |
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R Square Change |
F Change |
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1 |
.388a |
.150 |
.150 |
.91912 |
.150 |
462.783 |
Table 1: regression summary with the dummy variables included.
With the inclusion of the dummy variables, the model explains up to 15% of the variance in estimating Mathematics utility (slightly higher than the 14.8% explained with the exclusion of the dummy variables).
The model is significant (p < 0.05) and, therefore, the null hypothesis is that there is no linear relationship between the dependent variable and the independent variables (including the dummy variables) is rejected.
To further examine this relationship, the regression model is estimated.
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Coefficientsa |
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Model |
Unstandardized Coefficients |
Standardized Coefficients |
t |
Sig. |
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B |
Std. Error |
Beta |
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1 |
(Constant) |
.040 |
.022 |
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1.853 |
.064 |
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T1 Scale of student's mathematics identity |
.148 |
.008 |
.149 |
17.873 |
.000 |
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T1 Scale of student's mathematics self-efficacy |
.283 |
.008 |
.282 |
33.866 |
.000 |
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dummy 1 |
-.119 |
.025 |
-.057 |
-4.851 |
.000 |
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dummy 2 |
-.087 |
.025 |
-.040 |
-3.476 |
.001 |
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dummy 3 |
-.073 |
.028 |
-.026 |
-2.621 |
.009 |
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dummy 4 |
.001 |
.033 |
.000 |
.016 |
.987 |
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dummy 5 |
.039 |
.041 |
.007 |
.954 |
.340 |
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a. Dependent Variable: T1 Scale of student's mathematics utility |
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Table 2: Regression coefficients table.
With focus on the dummy variables included in the estimation of the regression model, two dummy variables are insignificant in the model (p-value > 0.05) and therefore are excluded from the final estimated model. The variables “between 3 to 4 hours” and “between 4 to 5 hours” are significant in estimating Mathematics utility model.
The coefficients of the model are as indicated in the table.
For the dummy variables, the arbitrarily chosen reference variable was “more than 5 hours” category. Therefore, watching movies and TV for less than an hour during typical school day negatively affects mathematics utility by 0.119 unites lesser than watching for more than 5 hours. Moreover, students who watch TV and movie for between 1 hour and 2 hours on typical schooldays will have their mathematics utility by 0.087 units lesser than those who watch for more than 5 hours, while those who watched for between 2 hours and 3 hours have 0.073 unites lesser effect than those who watched TV for more than 5 hours on a typical school day.
This predictive model could help in improving Mathematics performance of students by gauging their utility.
References
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Cohen, P., West, S. G., & Aiken, L. S. (2014). Applied multiple regression/correlation analysis for the behavioral sciences. Psychology Press. Frankfort-Nachmias, C., & Leon-Guerrero, A. (2017). Social statistics for a diverse society. Sage Publications. Passolunghi, M. C., Caviola, S., De Agostini, R., Perin, C., & Mammarella, I. C. (2016). Mathematics anxiety, working memory, and mathematics performance in secondary-school children. Frontiers in psychology, 7, 42.
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