Question

Based on the statistical data obtained from survivors countries in South America through the Population Reference Bureau (2013) and World Bank (2015), please analyze the relationship between Gross National Product (GNP) and infant mortality rates per 1,000 births.

Country	GNP Per Capita in 2013(X100)	Infant Mortality in 2013
Argentina	80.30	19.0
Bolivia	10.10	61.0
Brazil	46.30	33.0
Chile	49.90	10.0
Colombia	27.40	23.0
Ecuador	15.20	32.0
Paraguay	17.60	24.0
Peru	24.40	40.0
Uruguay	60.70	16.0
Venezuela	35.30	21.0

1. What is the r value for the relationship between the data distributions above?

2. What is the proportion of variance accounted for?

3. In your own words but based on the strength and direction of the relationship you calculated, explain the relationship between Gross National Product and infant mortality.

Answer 1

1.

The provided data are shown in the table below

X	Y
80.3	19
10.1	61
46.3	33
49.9	10
27.4	23
15.2	32
17.6	24
24.4	40
60.7	16
35.3	21

Also, the following calculations are needed to compute the correlation coefficient:

	X	Y	X*Y	X2	Y2
	80.3	19	1525.7	6448.09	361
	10.1	61	616.1	102.01	3721
	46.3	33	1527.9	2143.69	1089
	49.9	10	499	2490.01	100
	27.4	23	630.2	750.76	529
	15.2	32	486.4	231.04	1024
	17.6	24	422.4	309.76	576
	24.4	40	976	595.36	1600
	60.7	16	971.2	3684.49	256
	35.3	21	741.3	1246.09	441
Sum =	367.2	279	8396.2	18001.3	9697

The correlation coefficient r is computed using the following expression:

Therefore, based on this information, the sample correlation coefficient is computed as follows

2.

To calculate the proportion of variance accounted for we would rely on the coefficient of determination

Only 39.56% variation is accounted for in the model,

3.

The relationship between Gross National Product and infant mortality shows a negative association which is moderate in nature. They show a moderate linear negative relationship.

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