Question

The World Bank collected data on the percentage of GDP that a country spends on health expenditures ("Health expenditure," 2013) and also the percentage of woman receiving prenatal care ("Pregnant woman receiving," 2013). The data for the countries where this information is available for the year 2011 are in table #10.1.8. Find the correlation coefficient and coefficient of determination and then interpret both.

HEALTH EXPENDITURE (% of GDP)	Prenatal Care (%)
9.6	47.9
3.7	54.6
5.2	93.7
5.2	84.7
10.0	100.0
4.7	42.5
4.8	96.4
6.0	77.1
5.4	58.3
4.8	95.4
4.1	78.0
6.0	93.3
9.5	93.3
6.8	93.7
6.1	89.8

Answer 1

	HEALTH EXPENDITURE (% of GDP) (X)	Prenatal Care (%) (Y)	X * Y	X2	Y2
	9.6	47.9	459.84	92.16	2294.41
	3.7	54.6	202.02	13.69	2981.16
	5.2	93.7	487.24	27.04	8779.69
	5.2	84.7	440.44	27.04	7174.09
	10	100	1000	100	10000
	4.7	42.5	199.75	22.09	1806.25
	4.8	96.4	462.72	23.04	9292.96
	6	77.1	462.6	36	5944.41
	5.4	58.3	314.82	29.16	3398.89
	4.8	95.4	457.92	23.04	9101.16
	4.1	78	319.8	16.81	6084
	6	93.3	559.8	36	8704.89
	9.5	93.3	886.35	90.25	8704.89
	6.8	93.7	637.16	46.24	8779.69
	6.1	89.8	547.78	37.21	8064.04
Total	91.9	1198.7	7438.2	619.77	101110.5

correlatioon of coefficient

Interpretation :- The value of r is positive the range of r is -1 to 1, here r = 0.1715

We can say that there is positive but weak relation between the two variables ( HEALTH EXPENDITURE (% of GDP) &  Prenatal Care (%) )

Correlation of Determination R = r² = ( 0.1715 )² = 0.0294

To find the percentage 0.0294 * 100 = 2.94 %

We can say that 2.94% of variation in  HEALTH EXPENDITURE can be explained by Prenatal Care.