2012 H2 Maths Prelim Solution: SRJC/II/8(iv)

8(iv)

Using the model \displaystyle y=a+\frac{b}{x-2}, estimate the total fertility rate for a particular country Z when its GDP per capita is USD$1000, giving your answer to 1 decimal place and comment on the reliability of the estimate.

First, we need to remove the outlier (40,6.6) as mentioned in part iii.

Then, performing linear regression with GC, (with variables \frac{1}{x-2}y), we get:

a=0.974686

b=6.86442

Substituting x=1, we get \displaystyle y=a+\frac{b}{1-2}=-5.9 (1 d.p.)

Since we cannot have a negative fertility rate (the average number of children that would be born to a woman ), the estimate obtained for y is not reliable.