In the 1950s, retrospective cohort studies of smoking status and lung cancer outcomes showed "more heavy smokers and fewer non-smokers among patients with lung cancer than among patients with other diseases." Consider the following table that compares lung cancer patients with control patients categorized by the average number of cigarettes smoked daily. Group # of Cigarettes Lung Cancer Control None 7 61 < 5 55 129 5-14 489 570 15-24 475 431 25-49 293 154 50 38 12 (a) [3 marks] Fit independent and saturated models to these data. Is there sufficient evidence to indicate that there is a relationship between cigarette consumption and having or not having lung disease? Interpret your results. "None" and "Lung cancer " are reference levels. (b) [2 marks] Find all odds and confidence intervals related to the number of cigarettes from the independence model. (c) [2 marks] Find odd ratios and confidence intervals from the saturated model.