Multiple Regression

Instruction: Respond to at least one of your colleagues’ posts and comment on the following:
Do you think the variables are appropriately used? Why or why not?
Does the addition of the control variables make sense to you? Why or why not?
Does the analysis answer the research question? Be sure and provide constructive and helpful comments for possible improvement.
If there was a significant effect, comments on the strength and its meaningfulness.
As a lay reader, were you able to understand the results and their implications? Why or why not?

 

 

Sudent’s response: Research Question

Using the Afrobarometer dataset, this paper seeks to answer the research question: Is the level of trust in the African government influenced at all by the level of poverty level or the age of its citizens? The research hypothesis states that the level of trust in the government of Africa is associated with the level of poverty and the age of its citizens, and that the variables have a measurable influence on the level of trust. The null hypothesis therefor states that there is no association between the level of trust and the level of poverty or age of the citizens.

Research Design

According to the U.S. Department of State (n.d.), apartheid was a system of racial segregation that was predominant in South Africa from 1948 to the early 1990s. The brutal enforcement of draconian-style laws led to the rapid decline in the trust of the African government. Often, police forces are considered to be synonymous with the government. A logical research design to evaluate if the level of trust in the African government was affected by the age of its citizens, or their level of poverty, is conducted by gathering the data through the reported populations. The African census would serve to gather the mean age of the respondents and poverty levels could be obtained through any number of social service platforms and functions. The researchers would then query the level of trust of the government from respondents that reported a level of poverty, and compile the data for further analysis through a multiple regression evaluation.

Variables

Before proceeding with the examination, it is important to understand the variables and what data they represent. The dependent variable is the TRUSTGOV (Trust in Government Index) metric variable. The variable captures data on a scale of 1-15 in which the higher score represents more trust. The mean of this variable is 8.01. The first independent variable is the LIVEDPOVERTY (Lived Poverty Index) metric variable. This variable requests the respondent to answer on a scale of 1-5 how many basic necessity items the respondent went without during the previous year. The mean of this variable is 1.26. In this case, the higher score represents a greater level of poverty. The second independent variable is the Q1 (Age) metric level variable. This variable is captured by the biographical section of the survey in which the respondent enters their age. The mean of this variable is 37.14. These variables lead to the hypothesis that greater levels of poverty would be indicative of less trust in the government which would be indicated by an inversely proportionate negative relationship.

Variable Analysis

The SPSS multiple regression function provides the mechanism in which one can determine if the level of trust in the government has any relationship with the level of poverty or age of its citizens. According to Laureate Education (2016), the multiple regression is built on bivariate regression simply by adding more variables to the equation. The model summary data of the multiple regression is reflected in Table 1.

Table 1. Model Summary

 

Model

 

R

 

R Square

 

Adjusted R Square

 

Std. Error of the Estimate

 

1

 

.095a

 

.009

 

.009

 

4.18117

 

a. Predictors: (Constant), Lived Poverty Index (average index of 5 poverty items), Q1. Age

 

Table 1 identifies the simplistic model summary of the multiple regression. It demonstrates that the large R is equal to .095. The R square statistic of .009 provides more information about the model. From this value, an inference can be made that less than one-percent of the respondent’s level of trust in the government can be explained by their poverty level and age. In this case, the adjusted R square is the same as the R square, and while it is safer to use an adjusted R square when using multiple predictors (Laureate Education, 2016) the fact both are the same negates this measure. The analysis of the data presented in Table 1 allows for the interpretation that as less than one-percent (.009) of the variability in the respondent’s level of trust in the government is explained by the level of poverty or age of the respondent.

The next set of data prepared for analysis is from the ANOVA test. This tests for the overall significance of the regression model and is displayed in Table 2. Observation of the significance level of less than .000, which is well below the .05 threshold (ASA, 2016) which further allows for the conclusion that the model has statistical significance.

Table 2. ANOVAa

 

Model

 

Sum of Squares

 

df

 

Mean Square

 

F

 

Sig.

 

1

 

Regression

 

1213.497

 

2

 

606.748

 

34.707

 

.000b

 

Residual

 

132112.548

 

7557

 

17.482

 

 

 

 

 

Total

 

133326.044

 

7559

 

 

 

 

 

 

 

a. Dependent Variable: Trust in Government Index (higher scores=more trust)

 

b. Predictors: (Constant), Lived Poverty Index (average index of 5 poverty items), Q1. Age

 

The final set of data allows for the interpretation of coefficients and is displayed in Table 3. Table 3 provides several statistics to include the interpretation of the independent variables (Lived Poverty Index and Age). This data can be interpreted as for every single unit of increase in the independent variable Age, the dependent variable will change by the value of .026. For every single unit of increase in the independent variable Lived Poverty Index, the dependent variable will change by the value of -.199. The Standardized Coefficients value, or Beta, is .087 for Age and -.045 for the Lived Poverty Index. Also noteworthy is the p-value as continued to be reported as less than .000, also well below the .05 threshold for significance (ASA, 2016), which also forces a rejection of the null hypotheses.

Table 3. Coefficientsa

 

Model

 

Unstandardized Coefficients

 

Standardized Coefficients

 

t

 

Sig.

 

B

 

Std. Error

 

Beta

 

1

 

(Constant)

 

7.312

 

.145

 

 

 

50.304

 

.000

 

Q1. Age

 

.026

 

.003

 

.087

 

7.566

 

.000

 

Lived Poverty Index

 

-.199

 

.051

 

-.045

 

-3.903

 

.000

 

a. Dependent Variable: Trust in Government Index (higher scores=more trust)

Conclusion

In conclusion, while the data suggests there to be a statistically significant relationship between the variables, the strength of that relationship is relatively minor and would have little effect on the dependent variable. It appears as though the higher the level of poverty indicated a lower level of trust in the government, and the level of trust in the government tended to increase with the age of the respondent.

References

American Statistical Association. (2016). American statistical association releases statement on statistical significance and p-values. Retrieved from https://www.amstat.org /asa/files/pdfs/P-ValueStatement.pdf

Frankfort-Nachmias, C., Leon-Guerrero, A., & Davis, G. (2020). Social statistics for a diverse society (9th ed.). Sage Publications.

Laureate Education (Producer). (2016). Multiple regression [Video file]. https://class.content.laureate.net/74d592f154f1aae14924391224e45b82.html#section_container0

U.S. Department of State. (n.d.). https://2001-2009.state.gov/r/pa/ho/time/pcw/98678.htm