The data set infmort from the faraway package contains information on the mortality of infants for 105 nations. The variable mortality gives the number of deaths per 1000 live births, while income is the per capita income in us dollars and region indicates the geographic area of the nation. Consider the model e(log(mortality)|income, region) = β0 + β1 log(income) + β2region + β12region ∗ log(income).
(a) State the null and alternative hypotheses for the overall f-test for this model. Perform the test and summarize results
(b) Explain the practical meaning of the hypothesis h0 : β12 = β2 = 0 in the context of the above model.
(c) Perform a test for the hypothesis in part b) and summarize your results.