Linear Regression Analysis For Enrolment Rate Based On Independent Variables

Data collection and characteristics of data

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. 

Enrolment rate in school is one of the main concerns in today’s 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. 

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)”. 

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 country’s 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.

Variables

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.

The hypothesis of the test is as follows:

The null hypothesis is H₀ : β_j = 1, j = 1, 2, 3 and the alternative hypothesis is H₁: β_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. 

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.

Hypothesis

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 time 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.

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. 

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.