Write the cipher in RStudio to break the questions. Post all the codes in a document.
1. In a abstraction analytical smoker and lung cancer, a accidental sample of men amid the ages of 55 and 60 was obtained. The smoker and ache cachet of anniversary sampled accountable was ascertained. For anniversary subject, a ’1’ is assigned if the accountable had lung blight (case) and a ’0’ if not. Similarly, a ’1’ indicates that a accountable is a smoker and a ’0’ indicates a nonsmoker. The abstracts are begin in the Excel book ‘LungCancer’. • Read the abstracts into R, and use table() action to aftermath a accident table summarizing these data. • Assuming that there is no affiliation amid smoker and lung cancer, compute a table of ‘expected’ counts. • By hand, compute the empiric amount of the analysis accomplishment for testing affiliation amid lung blight and smoking. • Assuming there is no association, what is the administration of the analysis statistic? • Application R, compute the p-value for a analysis of association, and accord a abundant cessation based on the p-value and a allegory of the tables empiric and accepted counts. 2. The afterward abstracts are from a abstraction analytical the accident of tuberculosis in affiliation to claret groups in a sample of Eskimos. It is of absorption to actuate if there is any affiliation amid the ache and claret accumulation aural the ABO system. Severity O A AB B Moderate-advanced 7 7 7 13 Minimal 27 34 12 18 Not Present 55 52 11 24 • Assuming that there is no affiliation amid ache and claret group, compute a table of ‘expected’ counts. • By hand, compute the empiric amount of the analysis accomplishment for testing affiliation amid ache and claret group. • Assuming there is no association, what is the administration of the analysis statistic? • Application R, compute the p-value for a analysis of association, and accord a abundant cessation based on the p-value and a allegory of the tables empiric and accepted counts.
4. The book ‘growth’ gives abstracts on the acme of a white bandbox timberline abstinent annually for 50 years. Letting Yt denote the acme of the timberline at year t > 0, we accede anecdotic the advance of the timberline over time with a non-linear archetypal Yt = f(t) + ²t , ²t iid∼ N(0, σ2 ). Three advance curves are advised for f(t) (a) Logistic: f(t) = a/(1 + b ∗ exp{−ct}) (b) Gompertz: f(t) = a exp{−b exp{−ct}} (c) Von Bertalanffy: f(t) = a − a exp{−b(t + c)} • Fit all three models application the non-linear atomic squares action nls() in R. Explain how you are allotment the starting ethics for nls() in anniversary case. Aftermath a amount depicting the estimated curves all on the aforementioned plot, forth with the empiric data. Be abiding to accommodate a fable to analyze the altered curves. • For anniversary of the three models, accord a 95% aplomb breach for limt→∞f(t). What does this represent? • Select the best of the three models, and artifice an appraisal of the acquired df(t) dt , which represents the amount of advance over time.

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