Wednesday, May 6, 2020
Enrolment Rate in School
Question: A Linear regression estimation based on enrollment rate as dependent variable. Independent variables are governments expenditure, labor force with primary school, literacy rate. You need to provide data resources and a excel table for data. The independent variable is not limited. You can find any variable that is correlated to enrolment rate. Answer: Introduction Enrolment rate in school is one of the main concerns in todays world. Primary education is essential for the children in order to have a better life style. Enrolment rate varies for different factors. Enrolment rate in primary schools depends on factors like governments expenditure on primary education, labour force with primary school and the literacy rate of the country (Draper and Harry). In this assignment, the dependent variable is enrolment rate would be modelled, hypothesized and analysed depending on the other variables. Linear regression analysis would be performed and the model would be framed (Harrell). Each of the variables would be defined in this assignment and hypothesis would be stated. Thus, analysis of the variables and framing the model would help to infer about the data set using linear regression method. Data collection and characteristics of data The data for the independent variables and the dependent variables was collected from the data of world data bank. The data for literacy rate was collected from a journal, which researched, on the topic of literacy rates of the country. Data for 50 years were chosen for this assignment. The collected data contains one dependent variable of gross enrolment ratio, primary and there independent variable of literacy rate, governments expenditure and labour force with primary school (% of total). Variables The dependent variable of this assignment is gross enrolment ratio, primary. This variable defines the enrolment of students in primary schools. This variable gives the number of students who have enrolled in primary schools for the last fifty years. This variable gives an idea about the trend of education among the citizens to the USA (Seber and Alan). This gives an idea about the interest of the citizens of the country to educate their children in the future. The next variable literacy rate is the independent variable of the assignment. This variable gives an idea about the percentage of population above seven years of age who can read and write with understanding. This rate provides an idea about the educative percentage of the countrys population. The third variable is the governments expenditure which is another independent variable of the assignment. This variable provides information about the amount of money the government of United States had spent for education over the past fifty years. This variable would help to understand the importance of education in a country. This variable would also give information about the funds spent by the government to educate the people and the trend of education of the country (Montgomery et al.). The fourth variable of the assignment, labour force with primary school (% of total) gives an idea about the percentage of students who dropped out of the primary schools. This variable would give an idea about the education of the children of the country. The drop out from the school may be due to various reasons. This could be the cause of poverty or lack of proper guidance of study (Seber and Alan). Thus, the idea of the trend of education would be known from this variable. These four variables would be used to frame a linear regression model. Hypothesis would be set in order to study the effect of the variables. Hypothesis would be tested by using the linear regression model and conclusions would be drawn thereafter. Hypothesis The hypothesis of the test is as follows: The null hypothesis is H0 : j = 1, j = 1, 2, 3 and the alternative hypothesis is H1: j !=1 ; j = 1, 2, 3 This null hypothesis is simple hypothesis and the alternative hypothesis is composite hypothesis. This hypothesis would test find whether the dependent variable is linearly dependent on the independent variables or it is non-linearly dependent on the independent variables. Model description The model for this data set was found to be y = 65.10643 -0.00082 X1 + 2.71239 X2 -0.28907 X3. Here, y is the gross enrolment ratio, primary, X1 is the literacy rate, X2 is the governments expenditure and X3 is the labour force with primary school (% of total). From the model it can be seen that the gross enrolment ratio, primary would be 65.10643 in absence of all the factors of literacy rate, governments expenditure and labour force with primary school (% of total) (Harrell). The slope of literacy rate was seen to be decreasing. This suggests that the literacy rate of the country decreased with time. Earlier there was high literacy rate, but with time, the literacy rate had decreased. It was also seen that the literacy rate had decreased in the last year. This can be a concern for the future of the education of the country. This can be the effect of increase in population and the disruptions in the ratio between the population and education. From the model it can be seen that the slope of the governments expenditure had increased with time. This suggests that the government is willing to spend more money on education. This is a positive sign for the development of the country (Fox). This is because the more the government spends on education of the country; it would increase the literacy rate of the country. The government could develop the infrastructure of the educative institutions by investing more in education. Parents would send their children to schools and the children could have the basic education if the government provides them with funds and facilities. Thus, this is a good indication for the education of the country. The slope of the fourth variable, labour force with primary school (% of total)was found to be negative. Labour force with primary school (% of total) indicates the percentage of student who had dropped out of the school without completing their primary education (Draper and Harry). The lower the rate, the better is the education and facilities of the country. It is found that poverty or some other causes like family pressure or lack of opportunities and facilities force children to quit their primary education and support their family. This is a bad indication for the development of the country. Less is the labour force better is it for the country. In this model, it was seen that the labour force decreased with time as it shows a negative slope (Cameron and Pravin). This could be interpreted that earlier there were more number of students who left their primary education. This rate of leaving the primary education can be the affect of various reasons. This rate had decreased over t ime and it could be interpreted that the primary school dropouts had decreased over time and people send their children to primary schools to have a basic education. This is a good sign of development in the country. Interpretation of hypothesis test The value of the significant f of this test is less than the alpha level of significance of 0.05. This can be interpreted that the p value is greater than the significant f and the null hypothesis is accepted. Thus, it can be seen that the model is a linear model and this is the best-fit model for the data set. Table of analysis Regression Statistics Multiple R 0.87377 R Square 0.763474 Adjusted R Square 0.748376 Standard Error 3.505553 Observations 51 ANOVA df SS MS F Significance F Regression 3 1864.343 621.4477 50.56984 9.44E-15 Residual 47 577.5783 12.2889 Total 50 2441.922 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Lower 95.0% Upper 95.0% Intercept 65.10643 6.014165 10.82552 2.33E-14 53.00749 77.20537 53.00749 77.20537 literacy rate -0.00082 0.004318 -0.19063 0.849638 -0.00951 0.007864 -0.00951 0.007864 governments expenditure 2.71239 0.377373 7.187553 4.25E-09 1.953213 3.471567 1.953213 3.471567 labor force with primary school (% of total) -0.28907 0.067443 -4.28613 8.95E-05 -0.42475 -0.15339 -0.42475 -0.15339 Table 1: Regression table analysis (Source: created by author) Conclusion The model of regression was framed using the four variables. There was one dependent variable and three independent variables. Regression model was framed from the data set. Hypothesis was framed from the data set. This hypothesis was tested using the regression model. It was found that the model was a best-fit model. The type of dependency of the dependent variable on the independent variables was tested and it was found that the literacy rate and labour force with primary school decreased with time. This suggests that the gross enrolment rate had increased with time. But decrease in literacy rate is a concern for the government. This can be the effect on disruption in the proportion of population and available number of primary schools. References Cameron, A. Colin, and Pravin K. Trivedi.Regression analysis of count data. Vol. 53. Cambridge university press, 2013. Draper, Norman R., and Harry Smith.Applied regression analysis. John Wiley Sons, 2014. Fox, John.Applied regression analysis and generalized linear models. Sage Publications, 2015. Harrell, Frank.Regression modeling strategies: with applications to linear models, logistic and ordinal regression, and survival analysis. Springer, 2015. Montgomery, Douglas C., Elizabeth A. Peck, and G. Geoffrey Vining.Introduction to linear regression analysis. John Wiley Sons, 2015. Seber, George AF, and Alan J. Lee.Linear regression analysis. Vol. 936. John Wiley Sons, 2012.
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