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The Afro-barometer Dataset
QUESTION
Create a research question using the Afrobarometer Dataset or the HS Long Survey Dataset, that can be answered by multiple regression.
Use SPSS to answer the research question. Post your response to the following:
If you are using the Afrobarometer Dataset, report the mean of Q1 (Age). If you are using the HS Long Survey Dataset, report the mean of X1Par1Edu.
What is your research question?
What is the null hypothesis for your question?
What research design would align with this question?
What dependent variable was used and how is it measured?
What independent variables are used and how are they measured? What is the justification for including these predictor variables?
If you found significance, what is the strength of the effect?
Explain your results for a lay audience, explain what the answer to your research question.
| Subject | Statistics | Pages | 6 | Style | APA |
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Answer
Multiple Regression in the High School Longitudinal Dataset
Multiple linear regression is an improved form of simple or bivariate linear regression. In this case, the influence of more than one independent variable on a single dependent variable is examined (Wagner, 2016). Therefore, multiple linear regression analysis is associated with exploration of a single dependent or response variable and multiple/several independent or explanatory variables (Frankfort-Nachmias & Leon-Guerrero, 2017). In multiple regression model, two or more independent variables are used to predict the dependent variable. The general purpose of multiple regression is enhanced expositive examination of the relationship between several independent variables and a dependent variable, the model therefore is a linear expression of this relationship (Wagner, 2016). Multiple regression modelling is based on certain assumptions like linearity, homoscedasticity, non-multicollinearity and normality have to be made. This paper reports on a multiple regression analysis model formation based on the High School Longitudinal Survey Dataset.
High School Longitudinal Survey
It is a hypothetical thought that student’s ability is enhanced highly by psychological factors. This study examines answers to the question: What is the linear relationship between or effects of mathematics identity and mathematics self-efficacy on students’ Mathematics utility?
To answer this question, the null hypothesis being tested is that the slope of linear relationship between the dependent variable (mathematics utility) and dependent variables (mathematics identity and mathematics self-efficacy) is zero. That is, there is no linear relationship between the indicated dependent variable and the multiple independent variables. The regression model further assesses the level of association between these variable categories.
Experimental research design is ideal for this study as the causal relationship between the dependent variable and the multiple independent variables is assessed.
The dependent variable is ‘Mathematics Utility’ (‘X2MTHUTI’ measured as scale of Mathematics Utility’) which is a continuous variable of interval scale of measurement. The independent variables are ‘T2 Scale of student's mathematics identity’ and ‘T2 Scale of student's mathematics self-efficacy’ which are both continuous variables with Interval scale of measurement. The predictor variables are included in this question because they are interlinked with the predicted variable in the pedagogical realms.
Multiple Linear Regression
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Model Summaryb |
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Model |
R |
R Square |
Adjusted R Square |
Std. Error of the Estimate |
|
1 |
.450a |
.203 |
.203 |
.89858 |
Table 1: Regression model summary.
On the goodness of fit (R2), the model explains around 20% (20.3%) of the variation of the dependent variable (mathematics utility).
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ANOVAa |
||||||
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Model |
Sum of Squares |
df |
Mean Square |
F |
Sig. |
|
|
1 |
Regression |
3945.986 |
2 |
1972.993 |
2443.501 |
.000b |
|
Residual |
15521.515 |
19223 |
.807 |
|
|
|
|
Total |
19467.501 |
19225 |
|
|
|
|
Table 2: ANOVA table of the model.
This table indicates that the regression model is significant. Therefore, since p-value < 0.05, the null hypothesis of no linear relationship is rejected at 95% confidence level.
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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) |
-.020 |
.006 |
|
-3.073 |
.002 |
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T2 Scale of student's mathematics identity |
.306 |
.008 |
.309 |
39.085 |
.000 |
|
|
T2 Scale of student's mathematics self-efficacy |
.194 |
.008 |
.193 |
24.418 |
.000 |
|
Table 3: regression coefficients table.
The t-test shows the significance of each of the independent variables in predicting mathematics utility. The model, therefore, is:
Y = -0.020 + 0.306X1 + 0.194 X2 + 0.90
Where: Y denotes the “Mathematics utility” variable
X1 denotes the “Mathematics identity” variable
X2 denotes the “Mathematics self-efficacy” variable
The model, therefore, explains that a unit change in student’s Mathematics identity will effect a positive change of 0.306 units in the student’s Mathematics utility, while a unit change in the student’s self-efficacy will effect a 0.194 positive change in utility units. This model can be used to predict a student’s Mathematics utility when the independent variables in the model are measured.
Each of the independent variable is significant in the model. Hence, both the identity and self-efficacy variables are significant in modelling utility of a student in regards to the Mathematics subject.
This model is a significant effector in the social domain, especially in the psychological spectrum as Mathematics is an employing subject.
References
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Frankfort-Nachmias, C., & Leon-Guerrero, A. (2017). Social statistics for a diverse society. Sage Publications. Hanley, J. A. (2016). Simple and multiple linear regression: sample size considerations. Journal of clinical epidemiology, 79, 112-119. Wagner, W. E. (2016). Using IBM® SPSS® statistics for research methods and social science statistics (6th ed.). Thousand Oaks, CA: Sage Publications.
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