Question 2 The following data is a sample of 5 random countries. For each country we measure the following variables: . logPPgap: The logarithm of the 2001 gross domestic product per person in US dollars; . logFertility: The logarithm of the birth rate per 1000 females in the year 2000; . Purban: The percentage of the population which lives in an urban area. Name logFertility logPPgdp Purban Moldova 0.23 5.8 41 Netherlands 0.38 10.1 90 Estonia 0.14 8.3 69 Uganda 1.36 5.5 15 Hungary 0.13 8.6 65 We wish to predict logFertility using logPPgap and Purban, using a linear model y = XB+ with no constant (intercept) term. You are given the following R calculations. qt (0. 975, 1:5) ## [1] 12.706205 4.302653 3. 182446 2.776445 2.570582 qf (0. 95, 1, 1:5) ## [1] 161. 447639 18.512821 10.127964 7.708647 6. 607891 qf (0. 95, 2, 1:5) ## [1] 199.500000 19. 000000 9.552094 6.944272 5. 786135 (a) Calculate the least squares estimates of B. (b) Calculate the sample variance $2. (c) Calculate and interpret a 95% confidence interval for the parameter associated with Purban. (d) Test, at a 5% significance level, if there is a significant relationship between gross domestic product and fertility. (e) Test for model relevance at a 5% significance level. (f) Croatia has a gross domestic product of $4500 per person, and 58% of its population lives in an urban area. Calculate a 95% prediction interval for its birth rate