Question

The relationship between total fertility rate and prevalence of contraceptive practice was investigated for a large number of countries around the world. Measuring fertility rate in births per woman 15 to 49 years of age and the proportion of currently married women using a form of contraception as a percentage, the least-squares regression line relating these two quantities is y= 6.83-0.062x For the subset of 17 countries in the sub-Saharan region of Africa, fertility rate and the prevalence of contraceptive practice are:

country	fertrate	contra	country	fertrate	contra
Benin	7.1	9	Mali	6.7	5
Botswana	5	33	Nigeria	6.2	6
Burundi	6.8	9	Rwanda	8.5	10
Cameroon	6.4	2	Senegal	6.6	11
Cote d'Ivoire	7.4	3	Sudan	5.9	6
Ghana	6.4	13	Togo	6.2	34
Kenya	6.7	27	Uganda	7.3	5
Lesotho	5.8	7	Zimbabwe	5.7	43
Liberia	6.6	7

Measures of fertility rate are saved under the variable name fertrate, and values of percentage contraception under contra.

d) How do the actual fertility rates for the African nations compare with those that would be predicted based on the fitted regression line?

The equation for this is 6.94-0.0295x.. how was this calculated?

Answer 1

	Contra ( X )	Fertrate ( Y )	X * Y	X^2
	9	7.1	63.9	81
	33.0	5.0	165	1089
	9	6.8	61.2	81
	2	6.4	12.8	4
	3	7.4	22.2	9
	13	6.4	83.2	169
	27	6.7	180.9	729
	7	5.8	40.6	49
	7	6.6	46.2	49
	5	6.7	33.5	25
	6	6.2	37.2	36
	10	8.5	85	100
	11	6.6	72.6	121
	6	5.9	35.4	36
	34	6.2	210.8	1156
	5	7.3	36.5	25
	43	5.7	245.1	1849
Total	230	111.3	1432.1	5608

Regression equation is   

Where, a :- Y intercept

b :- Slope of the equation

to calculate the constants a and b

The regression equation of line becomes