# Regression Analysis (Coursework Sample)

I was asked to conduct a regression analysis using STATA

source..Factors Affecting Students’ Enrollment in Higher Learning Institutions

Name

Institution

Factors Affecting Students’ Enrollment In Higher Learning Institutions

Introduction

Evidence suggests that the rate of student's enrollment in higher education institutions in the united states depends on various factors (Bailey & Dynarski, 2011). Some of the factors that have been suggested to influence the students' enrollment rate include the level of income, cost of tuition, amount spend on boarding and accommodation and the government expenditure on higher education in the United States. Many research hypotheses have suggested that families' level of income affects the rate of enrollment in higher learning institutions. According to Haycock, Lynch & Engle, (2010), students from low-income families do not apply to some of the institutions that they have qualified for.

According to the research study conducted by Alecke, Burgard & Mitze, (2013), tuition fee has no significant effect on student’s enrolment in higher education institutions. However, a similar study conducted in Germany by Hübner, (2012) found that there is a negative impact of tuition fee on students' enrollment. That is, as the cost of tuition increases the number of students enrolling for higher education studied reduces. Other factors that are also associated with students' enrollment are government expenditure on higher education and the cost of boarding or rooms in schools and colleges.

Therefore, this research study, data obtained from secondary sources to investigate whether students’ enrollment in higher learning institution can be predicted by the cost of tuition, income level, government expenditure and cost of boarding. The data were analyzed using STATA and a regression model, presented below was formed.

Research objectives

The following objectives guided this research survey:

1 To investigate the effect of income level in GDP per capita in dollars on students’ enrollment in higher education institutions.

2 To investigate the effect of government spending on higher education on students’ enrollment in higher learning institutions.

3 To find out the effect of boarding and tuition fee on students’ enrollment in higher learning institutions in the United States.

Findings and Discussion

The regression analysis result obtained from STATA are presented below.

Figure 1: Scatter Plot showing the relationship between students' enrollment and Income level in GDP per capita

Figure 2: Regression coefficients

Table 1: Variables table for regression analysis

Variable

Names

Y

Students’ enrolled in higher education institutions

X1

Cost of Boarding and Rooms, dollars

X2

Tuition fee in dollars

X3

Income Level (GDP per capita), dollars

X3

Government spending on higher education in billion dollars

The general regression line is given below.

Y=a+b1X1+b2X2+b3X3+b4X4+e

Where: Y is the dependent variable,

a is the y-intercept, that is, an estimate of the value of Y when the Xi is zero,

e is the error term,

X1, X2, X3, and X4 are the independent variables

b1,b2,b3,b4 are the coefficient of the independent variables. bi measures the estimated change in Y as a result of one unit change in Xi.

Estimated regression line

The study developed an estimated regression line below based on the coefficient table obtained from STATA and presented in Figure 2 above.

Y=18.884+56.328X1+8.564X2+0.020X3-1060.568X4

The relationship between students’ enrollment in higher education institutions and the cost of boarding and rooms in dollars is positive. That is, the more, the higher the cost of boarding, the higher the number of enrollment. From the regression line, an additional one dollar on the cost of boarding results into an additional enrollment of 18 students.

On the other hand, the relationship between government spending on higher education in billion dollars and students’ enrollment in higher education institutions is negative. In other words, in government spending on higher education results in a decrease in the number of student's enrollment. According to the coefficient obtained in this study, an increase in government spending by one billion results in a decrease in a decrease in students' enrollment by 1060. However, the analysis presented herein did find this relationship statistically significant.

The cost of tuition and income level in GDP per capita are also positively associated with students’ enrolment. An increase in the cost of tuition by one dollar results into an increase in the number of enrollment by 56 students while an increase in the level of income by one dollar results into an increase in enrollment by eight students. However, both variables were not statistically significant at p=0.106 and p=0.197 respectively

Conclusion

The issue of college enrollment in the United States has been so inconsistent that it has attracted several research studies in the last three decades. The issue of enrollment into higher earning institutions is believed to be influenced by several factors. One of the factors that have been discussed as a significant factor influencing students' enrolment is the level of income of the family. According to Posselt, Jaquette, Bielby& Bastedo, (2012), low-income students' particularly from the Black and Latino ethnic groups are underrepresented in the United States' post-secondary schools, particularly the selective institutions.

According to the result of this study, the amount of family income positively influences the number of students enrolling in post-secondary institutions. In other words, the higher the amount of income, the higher the rate of enrollment. Although the result was no statistically significant, this study found that an increase in the amount of income by a dollar results into an increase in the number of enrollment by 0.02.

The other factor that influences the number of students enrolling for post-secondary education is the number of tuition fees. According to Stange, (2013), an increase in the amount of fee paid for tuition in post-secondary institutions is likely to affect (negatively) the number of students enrolling to the same institutions. However, a study by Hemelt & Marcotte, (2011) that used the data from all the public 4-year colleges and university from 1996 to 2006 found to sufficient evidence to conclude that an increase in the number of tuition results into a decrease in the number of students' enrolment into institutions of higher education.

In this study, the result was against the expectations. This study found that the number of students enrolling in higher learning institutions increases with an increase in the amount of tuition fee. Precisely, this study found that an increase in the amount of tuition fee paid in the institutions by one dollar results into an increase in the number of students enrolling higher learning institutions by eight students.

The variation on government spending in the post-secondary education in the United States have been found to have an impact on the behavior of students’ enrollment into the institutions. A research study conducted by McPherson & Schapiro, (1993) found the government expenditure influence the rate of enrollment in t

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