Question

Assume you are a Data Analyst in an international economic consultancy firm. Your team leader has given you a research task to investigate the empirical relationship between China’s export volumes and per capita GDP (Gross Domestic Product).

Relevant Variables: China’s Export volume index and China’s GDP per capita (constant 2010 US$).

(Annual time series data (for the period 1980 – 2018) from the World Bank - World development indicators database)

The data are stored in the file named “ASSIGNMENTDATA.XLSX” in the course website. Using EXCEL, answer below questions:

1. Using an appropriate graphical descriptive measure (relevant for time series data) describe the two variables (1 mark)

2. Use an appropriate plot to investigate the relationship between Export volume index and GDP per capita. Assume Export volume index as an independent variable. Interpret the plot.

3. Prepare a numerical summary report about the data on the two variables by including the summary measures, mean, median, range, variance, standard deviation, coefficient of variation, smallest and largest values, and the three quartiles, for each variable.

4. Calculate the coefficient of correlation (r) between Export volume index and GDP per capita. Then, interpret it.

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5. Estimate a simple linear regression model and present the estimated linear equation. Then, interpret the coefficient estimates of the linear model.

6. Determine the coefficient of determination R2 and interpret it.

7. Test whether GDP per capita positively and significantly increases with

export volume index at the 5% significance level.

8. What is the value of the standard error of the estimate (se). Then,

comment on the fitness of the linear regression model? (1 mark)

Country Name China

Year

Export volume index

GDP per capita (constant 2010 US$)

1980 7.190964398 347.1200879

1981 8.743517899 360.4279678

1982 9.428373444 386.8903417

1983 10.25153246 422.6591909

1984 12.34004595 480.3028638

1985 12.61492904 537.5026526

1986 15.52047929 576.9087566

1987 18.40145453 634.092911

1988 21.66725703 694.0647918

1989 22.42809652 712.1153633

1990 25.6864244 729.1606454

1991 29.44489072 786.1296588

1992 34.0846619 886.9503589

1993 37.95357331 998.4047893

1994 48.55720035 1116.032535

1995 56.85936289 1224.848821

1996 56.64713312 1332.417309

1997 67.91726097 1440.59025

1998 70.88444114 1538.662844

1999 77.44729803 1642.357488

2000 100 1767.833627

2001 109.694188 1901.40763

2002 138.6582488 2061.162284

2003 182.785201 2253.929689

2004 226.8347239 2467.132843

2005 283.6441931 2732.16588

2006 346.1719795 3062.534905

2007 414.8560285 3480.152725

2008 450.2958821 3796.633363

2009 403.192961 4132.902312

2010 516.4926068 4550.453596

2011 561.8922874 4961.234689

2012 596.8391727 5325.160106

2013 647.4202795 5710.587873

2014 684.4722854 6096.487817

2015 680.5921485 6484.435948

2016 690.2482661 6883.895425

2017 738.9259384 7308.065366

2018 769.5482696 7754.962119

Answer 1

1.

2. A scatter plot has been used to investigate the relationship between Export volume index and GDP per capita.

We can see a positive correlation in the data which means that an increase in the value of the independent variable, Export volumes results in an increase in GDP per capita value as well.

3.

Export volumes		GDP per capita
Mean	235.5547	Mean	2553.3020
Standard Error	42.1653	Standard Error	360.1313
Median	77.4473	Median	1642.3575
Standard Deviation	263.3223	Standard Deviation	2249.0190
Sample Variance	69338.6349	Sample Variance	5058086.3724
Kurtosis	-0.8622	Kurtosis	-0.3210
Skewness	0.8637	Skewness	0.9737
Range	762.3573	Range	7407.8420
Minimum	7.1910	Minimum	347.1201
Maximum	769.5483	Maximum	7754.9621
Sum	9186.6336	Sum	99578.7778
First quartile	24.0573	First quartile	720.6380
Second quartile	77.4473	Second quartile	1642.3575
Third quartile	432.5760	Third quartile	3964.7678
Coefficient of variatn	1.1179	Coefficient of variatn	0.8808

4.

Correlation

0.990116

There is a very high positive correlation between the two variables as was also seen from the scatter plot.

5.

Regression Statistics
Multiple R	0.9901155
R Square	0.9803288
Adjusted R Square	0.9797971
Standard Error	319.66841
ANOVA
	df	SS	MS	F	Significance F
Regression	1	1.88E+08	1.88E+08	1843.92	3.58819E-33
Residual	37	3780952	102187.9
Total	38	1.92E+08
	Coefficients	Standard Error	t Stat	P-value
Intercept	561.33041	69.08048	8.125746	9.5E-10
X Variable 1	8.4565136	0.196934	42.94089	3.59E-33

Estimated linear regression model: Y(GDP per capita)= 561.33041+ 8.4565 X(Export volumes)

6.

R Square

0.9803288

This suggests that the data is well fitted to the estimated regression line. It is the proportion of the variance in the dependent variable that is predictable from the independent variable.

8.

	Coefficients	Standard Error	t Stat	P-value
Intercept	561.33041	69.08048	8.125746	9.5E-10
X Variable 1	8.4565136	0.196934	42.94089	3.59E-33

From the p-value we can say that the intercept and the coefficient of X are both significant in the estimated regression.