WK10Assgn_Beal_R (7)

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1 Multiple Regression Testing Roswell Beal PhD of Science in Public Policy and Administration, Walden University Quantitative Reasoning and Analysis Professor Olivia Yu February 4th, 2024

2 An Example of Multiple Linear Regression Pt.1 Dataset Used: Afrobarometer Research Question: Does the “Number of Adults in Household” and “Lived Poverty Index” predict “Trust in Government”? Units of Analysis: Respondents Variables ● Dependent Variable: ○ Trust in Government Index ● Independent Variables: ○ Number of Adults in Household ○ Lived Poverty Index Null Hypothesis (H0): Number of Adults in Household and Lived Poverty Index are not significant predictors of Trust in Government index scores of respondents. Analytical Method/Design:A multiple linear regression will be used because all variables are continuous measures (Frankfort-Nachmias et. al., 2020). Results on Analysis Table 1. Regression Model

3 The effect size in Table 2 of the model is shown as Adj R²=.002, which indicates that the two predictors of Number of Adults in household and Lived Poverty Index explains 0.2% of the variances in Trust in Government index scores. The effect size is small in the model. Table 2. Table 3 shows that the regression model is significant, F(2,10784)=12.039, P<.001. This means that the null hypothesis is rejected due to the results. Table 3.

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4 Table 4 indicates that both of the independent variables in the model are significant since they are below (P<.05).Additionally, Lived Poverty Index is the stronger predictor at (β=-.035) while Number of Adults in household follows quickly behind at (β=-.030). As the Lived Poverty index score increases for respondents, Trust in the Government lowers. The same can be said for Number of Adults in a Household since the predictor is also negative. Table 4. Policy implication: If the Government wants to increase trust in their agency, they should perform further research to determine what intervention strategies will lower Lived Poverty Index scores and decrease the need for adults to share living spaces that result from poverty.

5 An Example of Multiple Linear Regression Pt. 2 Dataset Used: Afrobarometer Research Question: How does age and country by region explain respondents' feelings on the level of democracy today? Null Hypothesis: Age and Country by Region of respondents are not significant predictors of respondents perceived Level of Democracy: today. Variable Description ● Dependant Variable (Continuous): Level of Democracy: Today ● Independent variables: ○ Continuous: Age ○ Nominal: Country by Region Dummy Recoding: A multiple linear regression will be used to test the Null hypothesis. The nominal variable (Country.By.Region) is recoded into 3 dummy variables, each having two values (1/0). The three dummy variables are West_Africa, Eas_Africa and Southern Africa. Old Name New Name Recode Process Value Specification Country.By.Region West_Africa 1=1 All others=0 1=West Africa 0=All others Country.By.Region East_Africa 2=1 All others=0 1=East Africa 0=All others Country.By.Region Southern_Africa 3=1 All others=0 1=Southern Africa 0=All others Analysis

6 In this multiple linear regression, the dummy variable for North_Africa is excluded in the model as it is the reference for the dummy variables. Table 1 Variable entry In Table 2, the effect size of the model (Adj. R²=.008), which indicates that the model explains 0.8% of variances in Level of Democracy: Today score. Table 2 Table 3 shows that the model is significant, F(4,13046)=26.875, P<.001). This means that the null hypothesis is rejected due to the significance (Frankfort-Nachmias et. al., 2020). Table 3

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7 In Table 4, it is shown that the continuous variable is not significant at (β=.005), P<.543. The nominal variable that had the highest positive significance out of all the variables is Southern_Africa at (β= .142), P<.001 and an unstandardised B score of (P=.860). This was followed by West_Africa (P=.673) with β=.114 and East_Africa (P=.470) with β = .061. The model does not have multicollinearity since the dummy variables (West_Africa, East_Africa and Souther_Africa) variance inflation factors are shown as VIF Age = 1.001 which is closer to non correlation and the dummy variables being moderately correlated VIF West_Africa =2.720, VIF East_Africa =2.060 and VIF Southern_Africa =2.657. Table 4 Implications for Social Change An implication for social change of this example would be since county by region dummy variables show a more significant impact on respondents perception of the Level of Democracy: Today, further research is needed to determine what interventions are most

8 beneficial to increase those perceptions. This could include policy reform or social resources allocations or a combination of the two. However, further research can determine the best practices to increase the overall perceived level of democracy today. References

9 Frankfort-Nachmias, C., Leon-Guerrero, A., & Davis, G. (2020). Social statistics for a diverse society (9th ed.). Thousand Oaks, CA: Sage Publications. Walden University, LLC. (Producer). (2016). Dummy variables [Video file]. Baltimore, MD: Author. Walden University, LLC. (Producer). (2016m). Regression diagnostics and model evaluation [Video file]. Baltimore, MD: Author.

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