# 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:

•

•

•

•

•

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,…).

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.

•

•

•

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:

•

Recommend a course of action utilizing quantitative methods for health services including biostatistics,

forecasting, and the modeling of predictive functions.

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