Problem 3: In this problem we model data from a study of the prevalence of obesity, diabetes and cardiovascular disease among 403 African Americans in central Virginia. The data are in the diabetes dataset in the faraway library. One of the blood measurements is glycosolated hemoglobin (glyhb). A value higher than 7 is often considered to be a positive diagnosis for diabetes. Here we treat the numerical value og glyhb as the response, and consider possible predictor variables gender (a factor variable), waist, age, and stabilized glucose (stab. glu). a) Fit the ancova model that includes the main effects for gender, waist, age, stab. glu as well as the two-way interactions between gender and each of the other three predictor variables. Show the model summary and indicate which coefficients are significant at level 0.05. Answer:b) By comparing with a simplified model, test the null hypothesis that the three interaction coefficients all equal zero versus the alternative that at least one of them is nonzero. Use overall significance level of 0.05 and state your conclusion. Answer: c) The additive model has only the main effects; no interactions are included. (Main effects are terms involving only the original variables, not their products). Fit this model and determine which of the main effects appear to have statistically significant coefficients at the 0.05 level. Answer: d) Compute AIC for the model in a) and the model in c). Which model is preferred according to this criterion? Answer: e) Use the sequential analysis of variance table for the full model in a) to determine which main effects and interactions are significant. What do you conclude