Female education is especially important in developing countries. Research consistently shows that women who are empowered through education tend to have fewer children and have them later. If and when they do become mothers, they tend to be healthier and raise healthier children, who then also stay in school longer. To verify this hypothesis, a researcher gathered data about education and childbearing. The following table displays data on "the number of children per women" and percent of "primary school enrollment" in 15 developing countries.
|
ID
|
% Primary School Enrollment (X)
|
# of Children per Woman
(Y)
|
|
|
|
|
|
Ukraine
|
88
|
2
|
|
|
|
|
|
Kuwait
|
88
|
2
|
|
|
|
|
|
Iraq
|
85
|
5
|
|
|
|
|
|
Bangladesh
|
84
|
2
|
|
|
|
|
|
Albania
|
82
|
2
|
|
|
|
|
|
Armenia
|
82
|
3
|
|
|
|
|
|
Swaziland
|
80
|
5
|
|
|
|
|
|
Kenya
|
78
|
7
|
|
|
|
|
|
Nepal
|
69
|
6
|
|
|
|
|
|
Gambia
|
64
|
6
|
|
|
|
|
NOTE: use all columns to calculate components of regression and correlation. Add column if is needed. See the lecture note on regression and correlation
1. Find the mean ( X ¯= ∑X/N ) of each independent and dependent variable
2. Obtain the slope (b) and the y-intercept (a). Write the regression equation for the number of children (Y) and school enrolment(X)
3. Write the regression equation for # of children (Y) and school enrollment (X). How do you explain the relationship between X and Y?
4. Predict the number of children for a hypothetical country if the school enrollment would be 86
5. Use correlation formula to calculate the correlation between school enrollment and # of children per women. Show R and R2
6. What percentage of change in X explain change in Y?