EXERCISE 3 Consider the following two models: Y, = 263.6-0.005X -2.231X;2 adjR' =0.698 Y, =168.3-0.005X -1.768X2 +12.868X, adjR' = 0.734 Where Y = child mortality, X1= per capita income, X2 = female literacy rate, X3= fertility rate. All coefficients are statistically significant at the 5% level. a- Compare the two regressions. What changes do you see and what are they due to? b- Is it worth adding the variable X3? Why? How would you interpret its coefficient? C- If you were able to access data for all the variables above for 12 different countries and over a large number of years (say 100 years), how many dummy variables will you introduce to test the following hypotheses: i- Each of the 12 countries exhibits its own child mortality pattern. ii- 3 countries exhibit their own child mortality pattern while the other countries can be pooled into the same group d- You add one more variable to model 2 above and the result you get is as follows: Y, = 183.5 - 0.021X;1 - 8.143X12 + 7.84X13 - 2.31X13 All coefficients are statistically significant. According to this new model, it seems that after a certain level of fertility rate, the saturation level, more fertility does not lead to more child mortality. Find out what level of fertility that might be