For this first question, you will continue to use the dataset swiss which you also used in the last homework. Load the data. For more information about the data set, type ?swiss. The goal of the data set was to assess how fertility rates in the Swiss (French-speaking) provinces relate to a number of demographic variables. (a) In the previous homework, you fit a model with the fertility measure as the re- sponse variable and used all the other variables as predictors. Now, consider a simpler model, using only the last three variables as predictors: Education, Catholic, and Infant. Mortality. Carry out an appropriate hypothesis test to as- sess which of these two models should be used. State the null and alternative hypotheses, find the relevant test statistic, p-value, and state a conclusion in context. (For practice, try to calculate the test statistic by hand.)
(b) For the model you decide to use from part la, assess if the regression assumptions are met.