RStudio Data Analysis
RStudio Data Analysis.
Write the code in RStudio to solve the questions. Post all the codes in a document.
1. In a study examining smoking and lung cancer, a random sample of men between the ages of 55 and 60 was obtained. The smoking and disease status of each sampled subject was ascertained. For each subject, a 1 is assigned if the subject had lung cancer (case) and a 0 if not. Similarly, a 1 indicates that a subject is a smoker and a 0 indicates a nonsmoker. The data are found in the Excel file LungCancer . Read the data into R, and use table() function to produce a contingency table summarizing these data. Assuming that there is no association between smoking and lung cancer, compute a table of expected counts. By hand, compute the observed value of the test statistic for testing association between lung cancer and smoking. Assuming there is no association, what is the distribution of the test statistic? Using R, compute the p-value for a test of association, and give a detailed conclusion based on the p-value and a comparison of the tables observed and expected counts. 2. The following data are from a study examining the incidence of tuberculosis in relation to blood groups in a sample of Eskimos. It is of interest to determine if there is any association between the disease and blood group within 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 association between disease and blood group, compute a table of expected counts. By hand, compute the observed value of the test statistic for testing association between disease and blood group. Assuming there is no association, what is the distribution of the test statistic? Using R, compute the p-value for a test of association, and give a detailed conclusion based on the p-value and a comparison of the tables observed and expected counts.
4. The file growth gives data on the height of a white spruce tree measured annually for 50 years. Letting Yt denote the height of the tree at year t > 0, we consider describing the growth of the tree over time with a non-linear model Yt = f(t) + t , t iid N(0, 2 ). Three growth curves are considered 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 using the non-linear least squares function nls() in R. Explain how you are choosing the starting values for nls() in each case. Produce a figure depicting the estimated curves all on the same plot, along with the observed data. Be sure to include a legend to distinguish the different curves. For each of the three models, give a 95% confidence interval for limt f(t). What does this represent? Select the best of the three models, and plot an estimate of the derivative df(t) dt , which represents the rate of growth over time.
LungCancer.csv
3594.txt
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RStudio Data Analysis
