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                                                                                                                                             Introduction

 

The question the research paper is set to answer is whether or not there is any correlation between the percentage of international student enrollment in US and US’ Gross Domestic Product (GDP). Gross Domestic Product refers to the monetary value of finished goods and services produced within a country’s bounders in a year. Gross Domestic Product comprises the total consumption, investment, government expenditure and net export (Brezina, 2012). International student enrollment data provides the trend with which students’ exchange between countries have shaped out since 1948 (Hansel, 2007). The population of the data used for the analysis was the number of international students’ enrollment in the United States and the Gross Domestic Product of the United States per annum.

The sample data on students’ enrollment used in analysis was retrieved from a secondary source from the year 1948 to 2012 (Institute of International Education2012). The number of international student enrollment was given in thousand. Data on Gross Domestic Product used in the analysis was also obtained from a secondary source collected from the year 1948 to 2012. The value of the GDP was given in terms of trillions. The parameters used in the analysis were mean change in the number of international students’ enrollment in the United States and the mean value change of the Gross Domestic Product of the United States per annum.

            The statistic in the research paper was a mean of 7.5260 of the US’ Real Gross Domestic Product and a mean of .15375% of the number of students’ enrollment in the US per year. The standard deviation was 4.25723 of the US’ Real Gross Domestic Product and 0.0116131% of the number of international students’ enrollment in the US respectively.

            A hypothesis test was conducted in order to test the correlation between the percentage of international students’ enrollment and the Gross Domestic Product in US at 5% level of significance ( ᾳ= 0.05). The essence was intended to provide clear empirical evidence of any relationship that existed between the pair of variables described at 95% confidence interval. The statistical module used in the analysis was Pearson correlation coefficient. This is because Pearson correlation coefficient gives more accurate results as compared to other modules such as Spearman’s correlation coefficient and product-moment correlation coefficient. Statistical Product and Service Solution (SPSS) programmed was used for the analysis.

Data presentation

Years                                      Real US’ GDP                        % of int’l students’ enrollment in US

1948                                                    2.03                                         .0013

1949                                                    2.00                                         .0014

1950                                                    2.27                                         .0015

1951                                                    2.40                                         .0016

1952                                                    2.52                                         .0017

1953                                                    2.54                                         .0017

1954                                                    2.61                                         .0018

1955                                                    2.78                                         .0019

1956                                                    2.83                                         .0021

1957                                                    2.84                                         .0022

1958                                                    2.92                                         .0024

1959                                                    3.05                                         .0025

1960                                                    3.08                                         .0027

1961                                                    3.27                                         .0029

1962                                                    3.44                                         .0033

1963                                                    3.59                                         .0038

1964                                                    3.78                                         .0042

1965                                                    4.10                                         .0042

1966                                                    4.28                                         .0051

1967                                                    4.40                                         .0056

1968                                                    4.62                                         .0062

1969                                                    4.71                                         .0069

1970                                                    4.70                                         .0074

1971                                                    4.91                                         .0072

1972                                                    5.25                                         .0075

1973                                                    5.46                                         .0077

1974                                                    5.35                                         .0079

1975                                                    5.49                                         .0092

1976                                                    5.73                                         .0104

1977                                                    6.01                                         .0121

1978                                                    6.41                                         .0135

1979                                                    6.50                                         .0147

1980                                                    6.49                                         .0159

1981                                                    6.58                                         .0167

1982                                                    6.49                                         .0172

1983                                                    6.99                                         .0173

1984                                                    7.39                                         .0175

1985                                                    7.70                                         .0176

1986                                                    7.93                                         .0179

1987                                                    8.28                                         .0182

1988                                                    8.60                                         .0188

1989                                                    8.84                                         .0197

1990                                                    8.90                                         .0209

1991                                                    9.01                                         .0215

1992                                                    9.40                                         .0224

1993                                                    9.64                                         .0230

1994                                                    10.04                                       .0232

1995                                                    10.27                                       .0232

1996                                                    10.73                                       .0234

1997                                                    11.20                                       .0246

1998                                                    11.76                                       .0251

1999                                                    12.33                                       .0263

2000                                                    12.68                                       .0280

2001                                                    12.71                                       .0298

2002                                                    12.96                                       .0300

2003                                                    13.53                                       .0293

2004                                                    13.95                                       .0289

2005                                                    14.37                                       .0289

2006                                                    14.72                                       .0298

2007                                                    15.00                                       .0319

2008                                                    14.57                                       .0344

2009                                                    14.54                                       .0354

2010                                                    14.94                                       .0370

2011                                                    15.24                                       .0391

2012                                                    15.54                                       .0419

n= 64                                                   x= 7.5260                                y= 0.15375

Pearson correlation coefficient formula is given as

Where r denotes the Pearson coefficient

            n denoted the sample size

            x denotes the mean percentage of international students’ enrollment in US

            y denotes the mean value of Gross Domestic Product in the US

Since SPSS have built in commands, results were given based on the above formula. 

 

                                                           Results and Discussion

Reliability statistics

Cronbach's Alpha

N of Items

.711

2

 

            Cronbach’s Alpha =0.711 gives the reliability statistics. The value is positive due to a positive average covariance among items. This qualifies the reliability model assumptions. Therefore coding of the items in the codebook was done with at-most care. The results therefore obtained from this data, could be used for inference.

                                                             Correlation matrix

 

 

US Real GDP per year.

International students Enrollment Trends

US Real GDP per year.

 

Pearson Correlation

1

.985**

Sig. (2-tailed)

 

.000

Sum of Squares and Cross-products

1159.937

60939777.707

Covariance

18.124

952184.027

N

65

65

International students Enrollment Trends

 

Pearson Correlation

.985**

1

Sig. (2-tailed)

.000

 

Sum of Squares and Cross-products

60939777.707

3298273507597.753

Covariance

952184.027

51535523556.215

N

65

65

 

 

            The Pearson’s correlation coefficient r= 0.985. This shows that the correlation between the percentages of international students’ enrollment in US and the value of Gross domestic Product across the years is a strong positive correlation. In this respect, as the Gross Domestic Product increases over the years, the percentage of international student enrollment in the US increases as well. The results obtained above are significance at 5% level of significance since the p-value obtained is less than 5% i.e. (p-value= 0.001<ᾳ= 0.05). These results indicate that, at the bivariate level, each of the conditions necessary to test for the possible factors that influence the percentage of international students’ enrollment in the US.

Hypothesis test:

  1. 1.Ho: There is no correlation between the percentage of international students’ enrollment and the US’ Gross Domestic Product.

            H1: There is correlation between the percentage of international students’ enrollment and           the US’ Gross Domestic Product.

  1. 2.Ho: The value of the independent variable is zero

H1: The value of the independent variable is not zero

            The null hypothesis that was being tested stated that there is no correlation between the percentage of international students’ enrollment and the Gross Domestic Product of the US. From the results obtained, the null hypothesis is rejected. The positively strong Pearson’s correlation of 0.958 is statistically sufficient to conclude that the percentage of international students’ enrollment is highly related to the growth of the US’ Gross Domestic Product.

Model summary

Model

R

R Square

Adjusted R Square

Std. Error of the Estimate

Change Statistics

Durbin-Watson

R Square Change

F Change

df1

df2

Sig. F Change

1

.985a

.971

.970

.0020052

.971

2083.620

1

63

.000

.204

 

Predictor: (Constant), US Real GDP per year

Dependent variable: International students Enrollment Trends

            The table below presents a summary of the model obtained after the dependent variable is regressed against the independent variables. The R value= 0.985 gives the correlation of the entire model. The "adjusted R²" is intended to "control for" overestimates of the population R²= 0.970 resulting from small samples, high collinearity or small subject/variable ratios. Increasing value of R Squared implies decrease in estimation error. Since R squared= 0.828, then the estimation error of the model is minimal. The value of the Durbin-Watson shows that the results obtained are significant at 5% level of significance. The standard error of estimation is amounts to 0.0020052.

ANOVA table

 

Model

Sum of Squares

df

Mean Square

F

Sig.

1

Regression

.008

1

.008

2083.620

.000b

Residual

.000

63

.000

 

 

Total

.009

64

 

 

 

Dependent variable: percentage International students’ enrollment in US

Predictor: US Real GDP per year

            The table above presents the analysis of variance of the regression model against residual.  It was found that the overall model was significant at 5% level of significance. F( 1,63) =2083.62 with p-value of 0.001. This means that the hypothesis that the value of the independent variable equal to zero is rejected.

            In order to establish the relationship between the percentage of international students’ enrollment and the US’ Gross Domestic Product, linear regression coefficients were obtained. 

Coefficients

 

Model

Unstandardized Coefficients

Standardized Coefficients

t

Sig.

95.0% Confidence Interval for B

B

Std. Error

Beta

Lower Bound

Upper Bound

1

(Constant)

-.005

.001

 

-9.547

.000

-.006

-.004

US Real GDP per year.

.003

.000

.985

45.647

.000

.003

.003

Dependent variable: International students’ enrollment trends

            Gross Domestic Product significantly predicts the percentage of international students’ enrollment in US. t(1)= 45.647 with p-value= 0.001. The constant value= -0.005, is also significance at 5% level of significance. The 95% confidence interval also confirmed that the results obtained were significant. This is because the interval crosses the zero.  The model further predicted that for every unit increase in the Gross Domestic Product, the percentage of international students’ enrollment in US increased by 0.003.

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