MAT 543 SU Statistical Forecasting Case Study

Week 5 Assignment – Case Study: Statistical ForecastingDr. Megan Zobb, a key researcher within the North Luna University Medical Center, has
been studying a new variant of a skin disease virus that seems to be surfacing among
the North Luna University population. This variant (which has been tentatively named
Painful Rash or PR), leads to the formation of surface lesions on an individual’s body.
These lesions are very similar to small boils or isolated shingles sores. These PR
lesions are not necessarily clustered as shingles lesions are, but are isolated across the
body.
Insights From Initial Interviews
Megan is initiating some efforts at a preliminary analysis. She has seen 20 initial
patients and made several observations about the skin disease. She wants to analyze
this initial data before structuring and recommending a more encompassing study.
The signs and symptoms of this disorder usually affect multiple sections of the patient’s
body. These signs and symptoms may include:
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•
•
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Pain, burning, numbness or tingling, but pain is always present.
Sensitivity to touch.
A red rash that begins a few days after the pain.
Fluid-filled blisters that break open and crust over.
Itching.
Some people also experience:
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•
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Fever.
Headache.
Sensitivity to light.
Fatigue.
Pain is always the first symptom of PR. For some, it can be intense. Depending on the
location of the pain, it can sometimes be mistaken for a symptom of problems affecting
the heart, lungs, or kidneys. Some people experience PR pain without ever developing
the rash. The degree of pain that the individual experiences is seemingly proportional to
the number of lesions.
Dr. Zobb is extremely concerned that this new variant is especially challenging to the
younger population, who are active and like to be outdoors. She has asked you as an
analyst and statistician for some assistance in analyzing her initial data. She is not a
biostatistician, so she requests that you explain the process you use and your
interpretation of the results for each task.
Initial Data Analysis
Dr. Zobb has accumulated some data on an initial set of 20 patients across multiple age
groups. She believes that the data suggests younger individuals are affected more than
others. She wants you to complete the tasks shown here based on the data below.
For each of the following, provide a detailed explanation of the process you used along
with your interpretation of the results. Submit the response in a Word document and
attach your Excel spreadsheet to show your calculations (where applicable). Be sure to
number each response (e.g., 1.a, 1.b,…).
1.
2.
3.
Develop an equation to model the data using a regression analysis approach and explain your calculation
process in Excel.
Calculate the r-square statistic using Excel. Interpret the meaning of the r-square statistic in this case.
Determine three conclusions that address the initial observations and are supported by the regression
analysis.
Regression Analysis Initial Data
Patient
Number
Age of Patient
Number of
Lesions
1
24
16
2
63
7
3
45
12
4
17
24
5
21
20
6
72
4
7
32
13
8
36
16
9
26
21
10
47
10
11
31
15
12
23
18
13
51
8
14
24
22
15
26
18
16
25
19
17
31
12
18
19
29
19
18
25
20
21
17
Effects of Sunlight Analysis
In her initial observations, Dr. Zobb notices that the number of lesions that appear on a
patient seems to be dependent on the amount of direct sunlight exposure that the
patient receives. She is uncertain at this point why this would be the case, but she is a
good experimentalist and is trying to establish some observations that have statistical
validity. She has taken a limited amount of data on 8 patients and wants you to
complete the appropriate analysis based on the data below (be sure to show your
work):
1.
2.
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•
•
3.
Develop an equation to model the data using a regression analysis approach and explain your calculation
process, using Excel.
Megan has a small group of three additional patients that are the same age that she wants to examine for
lesions. She knows the number of minutes of continuous exposure to direct sunlight that each has
experienced. Predict the number of lesions that each of these patients will have based on the regression
analysis that you completed in your initial data analysis:
Patient 9 – 193 minutes.
Patient 10 – 219 minutes.
Patient 11 – 84 minutes.
Determine three conclusions based on the correlation of the number of lesions to minutes of sunlight
exposure, using regression analysis.
Sunlight Exposure Regression Data
Time of
Continuous
Exposure to
Direct Sunlight
(Minutes)
Number of
Lesions
1
225
24
2
184
16
3
220
20
4
240
26
5
180
14
6
184
16
7
186
20
8
215
22
Patient
Number
Over the Counter Medication Effectiveness Analysis
Dr. Zobb wants to test several over the counter lotions—that is, lotions available without
a prescription—that can be applied directly to the lesions. She wants to determine
whether there is a difference in the mean length of time it takes these three types of
pain lotions to provide relief from the pain caused by these lesions. Megan is hoping
that one of these lotions might be more promising than the others. Several sufferers
(with roughly the same number of lesions) are randomly selected and given one of the
three medications. Each sufferer records the time (in minutes) it takes the medication to
begin working. The results are shown in the table below. She asks you to answer these
questions (be sure to show your work).
1.
2.
3.
State the null hypothesis and the alternative hypothesis for this situation.
At α = 0.01, can you conclude that the mean times are different? Assume that each population of relief times is
normally distributed and that the population variances are equal. Hint: Use a one-way ANOVA to solve this
problem. Be certain to show your calculations and describe the process you used to solve this problem.
Determine three conclusions on the effectiveness of the medication by addressing observations or hypotheses
regarding these initial tests.
Effectiveness of Over the Counter Medications
Medication 1
(Minutes)
Medication 2
(Minutes)
Medication 3
(Minutes)
12
16
14
15
14
17
17
21
20
12
15
15
19
Summary of Data Analysis
Now that you have all of your data analysis:
1.
2.
Provide a three-paragraph summary of the findings you learned through the analysis.
Provide three data-driven suggestions for further exploration.
This course requires the use of Strayer Writing Standards. For assistance and
information, please refer to the Strayer Writing Standards link in the left-hand menu of
your course. Check with your professor for any additional instructions.
The specific course learning outcome associated with this assignment is:
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Recommend a course of action utilizing quantitative methods for health services including biostatistics,
forecasting, and the modeling of predictive functions.