STATISTICS 1403 CASE STUDY: ESTIMATING TUMOR WEIGHT 1

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)
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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