Sample The Correlation between Percentage of International Student Enrollment in US and the US' GDP
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 productmoment 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 atmost 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. (2tailed) 

.000 

Sum of Squares and Crossproducts 
1159.937 
60939777.707 

Covariance 
18.124 
952184.027 

N 
65 
65 

International students Enrollment Trends 

Pearson Correlation 
.985^{**} 
1 
Sig. (2tailed) 
.000 


Sum of Squares and Crossproducts 
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 pvalue obtained is less than 5% i.e. (pvalue= 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.Ho: There is no correlation between the percentage of international students’ enrollment and the US’ Gross Domestic Product.
H_{1: }There is correlation between the percentage of international students’ enrollment and the US’ Gross Domestic Product.
 2.Ho: The value of the independent variable is zero
H_{1}: 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 
DurbinWatson 

R Square Change 
F Change 
df1 
df2 
Sig. F Change 

1 
.985^{a} 
.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 DurbinWatson 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 
.000^{b} 
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 pvalue 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 pvalue= 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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