Statistical Forecasting on Painful Rash or PR

Dr. 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 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:
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:
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,…).
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):
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
Patient Number 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
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).
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:
Provide a three-paragraph summary of the findings you learned through the analysis.
Provide three data-driven suggestions for further exploration.