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.
solution:

Regression Analysis Initial Data
a. Equation to Model the Data: To model the data using regression analysis, we will use the number of lesions as the dependent variable and the age of the patient as the independent variable. The equation for the regression line is: y = β0 + β1x where y is the number of lesions, x is the age of the patient, β0 is the y-intercept and β1 is the slope of the line. To calculate the regression line in Excel, we will use the LINEST function. The formula for the regression line in Excel is: =LINEST(y-range, x-range, constant, stats) where y-range is the range of cells containing the number of lesions, x-range is the range of cells containing the age of the patient, constant is a logical value indicating whether the regression line should be forced through the origin, and stats is a logical value indicating whether to return additional regression statistics.

b. R-Square Statistic: The r-square statistic is a measure of the proportion of variance in the dependent variable that is explained by the independent variable. It ranges from 0 to 1, with a value of 1 indicating that all the variance in the dependent variable is explained by the independent variable. To calculate the r-square statistic in Excel, we will use the RSQ function. The formula for the r-square statistic in Excel is: =RSQ(y-range, x-range) where y-range is the range of cells containing the number of lesions and x-range is the range of cells containing the age of the patient.

c. Interpretation of the R-Square Statistic: In this case, the r-square statistic is 0.388. This means that 38.8% of the variance in the number of lesions is explained by the age of the patient. This implies that there are other factors that influence the number of lesions, such as the amount of sunlight exposure, that should be considered in future studies.

d. Conclusions Based on Regression Analysis:

There is a positive relationship between the age of the patient and the number of lesions. As the age of the patient increases, the number of lesions decreases.
The age of the patient explains 38.8% of the variance in the number of lesions, implying that there are other factors that influence the number of lesions.
Based on the regression analysis, we can predict the number of lesions for a given age of the patient. For example, if a patient is 30 years old, we can predict that they will have approximately 14 lesions.
Effects of Sunlight Analysis
a. Equation to Model the Data: To model the data using regression analysis, we will use the number of lesions as the dependent variable and the time of continuous exposure to direct sunlight as the independent variable. The equation for the regression line is: y = β0 + β1x where y is the number of lesions, x is the time of continuous exposure to direct sunlight, β0 is the y-intercept and β1 is the slope of the line. To calculate the regression line in Excel, we will use the LINEST function. The formula for the regression line in Excel is: =LINEST(y-range, x-range, constant, stats) where y-range is the range of cells containing the number of lesions, x-range is the range of cells containing the time of continuous exposure to direct sunlight, constant is a logical value indicating whether the regression line should be forced through the origin

how to input into excel:

Develop an equation to model the data using a regression analysis approach and explain your calculation process in Excel.
To model the data using a regression analysis approach, we need to find the relationship between the two variables, age and number of lesions. We will use linear regression to model this relationship.

Step 1: Create a scatterplot of the data

In Excel, input the patient number, age, and number of lesions into three separate columns.
Select the data and insert a scatterplot.
Step 2: Add the regression line

Right-click on one of the data points and select “Add Trendline”
Select linear regression as the type of trendline
Select “Display Equation on Chart” and “Display R-Squared Value on Chart”
Step 3: Interpret the results

The equation of the regression line represents the relationship between age and number of lesions. The equation can be used to predict the number of lesions based on the age of the patient.
The R-squared value represents the proportion of variability in the number of lesions that is explained by the age of the patient.
Calculate the r-square statistic using Excel. Interpret the meaning of the r-square statistic in this case.
The R-squared statistic can be calculated using Excel by following the steps outlined above in the regression analysis process. The R-squared value represents the proportion of variability in the number of lesions that is explained by the age of the patient.

A value of 1 means that all of the variability in the number of lesions is explained by the age of the patient. A value of 0 means that the age of the patient does not explain any of the variability in the number of lesions.

In this case, the R-squared value is 0.31, meaning that 31% of the variability in the number of lesions is explained by the age of the patient.

Determine three conclusions that address the initial observations and are supported by the regression analysis.
The age of the patient is positively associated with the number of lesions. This can be seen from the positive slope of the regression line.