Answer

Correlation and Bivariate Regression

#1: Research Question

What is the association between family incomes in constant dollars and the level of education attained?

#2: Hypotheses Statement

H₁: There is no association between family incomes in constant dollars and the level of education attained.

H₂: There exists an association between family incomes in constant dollars and the level of education attained.

#3 Research Design

             The framework created to find out the answer to the research questions involved employing secondary data on a quantitative study. The research data on family incomes in constant dollars and the level of education attained were collected from a secondary source.

             The research question focuses on associations among variables which is a test of the relationship of the variables. Therefore, correlation was used to test the association in order to show whether family income can relate with the level of education using a regression analysis. Correlation is an association of variables (McMaster, Rague, Wolthuis, & Sambasivam, 2018).

. According to Frankfort-Nachmias and Leon-Guerrero (2018), regression analysis is a measure on how a response variable changes relevant to the independent variable. The Author also states that correlation analysis is used to check on the relationship of the variables under study. A correlation value of 1 shows a perfect relationship and a 0 value of correlation means there change of one variable is not related to the change of the other.

Regression analysis contains the R square which shows how family income explains the level of education. R square shows if the equation has goodness of fit. ANOVA analysis was done to test the statistical significant in the regression equation that can be formed by the predictor and the response variables of study. P value is used to determine the confidence interval of a result of a test (Chapman, 2012). The p value was used to establish the level of statistical significance of the formed equation and the residuals at 99% level of significance.

#4 Dependent Variable Used

            The dependent variable, also called response variable, is predicted by an independent variable. In this case, there are two variables, namely between family incomes in constant dollars and the level of education attained. The level of education is expected to respond to the change in the family income. Therefore, the dependent variable is the level of education attained by the student. The variable is measured by the level of education attained.

#5 Independent Variable Used

The family income is expected to predict the level of education and hence, can be termed as the predictor variable. Predictor variable is the independent variable.  The independent or predictor variable is the family income of the respondent. The variable is measured by the amount of income in dollars that the family of the respondent has.

#6 The Results and Significance

The table below indicates correlation analysis between family incomes in constant dollars and the level of education attained. The results show a positive but weak correlation of 0.442. The result is an indicator that in as much as the association is weak, the increase of one variable parallels with an increase in the other.

The correlation result is statistically significant (P<0.01) and therefore there is an association between the variables, Pearson correlation being 0.442.

Regression Analysis

            The regression analysis indicates that F(1, 2312)=474.772, p<0.000, R square=0.170. This shows that there is an association between family incomes in constant dollars and the level of education attained is statistically significant (p<0.05).

The table below is the results on the residuals. The residuals table indicates that the weights by the independent variable income are statistically significant with both p<0.000 respectively. A unit change in family income causes a 2.881E-5 change in the level of education according to the results.

#7 Explanation of the Results

            The correlation and the bivariate regression are very important in finding out the association between variables. In this case the study sought to find out the association between family incomes in constant dollars and the level of education attained.

            The result of this study shows that the correlation is positive and weak. A correlation of more than 0.7 is known to be strong association and therefore for a change in one variable is sensitive to the change in the other. A correlation of 0.4 is regarded as low.

            The results shows that the regression equation is statistically significant with p<0.000, however, the low R square of 0.17 is an indicator of low good of fit in the equation. The good fit shows the percentage of variation of the dependent variable based on the independent variable (Wagner, 2016). Therefore, the family income is responsible for 17% variability of the level of education of individuals. According to Stoica 2013), a good fit is over 80%, yet again a low good fit does not mean the equation is not valid or the predictor variable is not effective.

In conclusion, although there is a weak association between family income and the level of education, family income shows significant effect on the level of education of an individual according to the study.