A study of the life expectancy of women was conducted in 12 Western Hemisphere coun- tries. The average number of children women gave birth to in these countries was also measured. The results are given below in Table 4.1, which contains the number of birth (x) and the life expectancy (y) in years for each of the 12 countries.
A simple linear regression model was fitted to the data in Table 4.1, which gives E(Y|X = x), the conditional expectation of the life expectancy, as a linear function of the number of births, x.
(a) By using the summary statistics in Table 4.1, produce an ANOVA table for this model and hence use an F test to test the hypothesis that the slope of the regression line is zero. [5 marks]
(b) Obtain point estimates for the three parameters of the above simple linear regression model. [5 marks]
(c) Test, using a Student's t test, the hypothesis that the slope is zero, for the above simple linear regression model. [5 marks]
(d) obtain a 95% confidence interval for the intercept parameter. [5 marks]
(e) Comment on the interval obtained for the intercept parameter. [5 marks]
