STATISTICS 1403 CASE STUDY: ESTIMATING TUMOR WEIGHT Abstract. Give a very short description of the research problem and methods here. 1. Background and Problems An experiment was conducted on 18 patients with cancer tumors. Each tumor was weighed, and measured for emitted radioactivity during the process of scintigraphic imaging. We would like to develop a linear regression model that would estimate the weight of a tumor, based on the emitted radiation. 2. Data Data from this experiment can be found in the ISDALSdata.xls worksheet under the cancer2 tab. 3. Proposed Analysis and Methods 3.1. Recommended MATLAB Functions. These MATLAB functions may be useful: log(), figure, scatter(), fitlm(), predict(), lillietest(); as well as these m-files: XYplots() and ResidualPlots(). Copy the code from XYplots and ResidualPlots and save them as .m files in the same folder as your script. Read about the MATLAB functions in the online MATLAB reference. Read about the m-files at their links: XYPlots() and ResidualPlots(). 3.2. Data Summaries, Estimates, Tests, and Models. This model for estimating mammalian brain weights is an example of the analysis you will perform. 3.3. Model Selection. Generate the set of scatterplots from XYplots.m, and use these to select candidate straight-line models. Show the plots. >> XYplots(radioact, tumorwgt) 3.4. Model Fitting and Diagnosis. Fit each of the candidate models using fitlm(), and check the resulting model for violations of the regression assumptions. Here is an example of the code for one of the models: >> >> >> >> >> >> linModel = fitlm(radioact, tumorwgt) scatter(radioact, tumorwgt) hold on plot(radioact, linModel.Fitted, ’--r’) hold off ResidualPlots(linModel) 1 2 ESTIMATING TUMOR WEIGHT 3.5. Model Selection. Based on the model F statistics, overall R-squared values, and p-values for the model coefficients, select the model that best fits the data. 3.6. Prediction. Using your selected model, predict the weight of a tumor with a radioactivity reading of 9.0. Give a 95% prediction interval >> predict(linModel, 9.0, ’Prediction’, ’observation’) Of course, if you select something other than the linear model, the Xnew = 9.0 may need to be modified accordingly. 4. Presentation Your completed report should include the following Abstract: a brief description of the problem and your recommended solution. Data: tell what the data represents, and display it graphically (a scatterplot is appropriate here) Model Selection: show the estimates and ANOVA from each candidate model, along with a fitted plot Prediction: give the point and interval estimates for the desired predicted value