Already solved just needs to be input into an excel spreadsheet and summarize
Sources for – Provide three data-driven suggestions for further exploration. are as follows
Solved information plus original question; tables for each part is attached.
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:
Some people also experience:
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.
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,…).
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:
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:
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
Step 2: Add the regression line
Step 3: Interpret the results
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.
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):
Sunlight Exposure Regression 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).
Step 2: Calculate the sum of squares (SS) for each medication: Medication 1: SS = (12-14)^2 + (15-14)^2 + (17-14)^2 + (12-14)^2 = 12 Medication 2: SS = (16-16.6)^2 + (14-16.6)^2 + (21-16.6)^2 + (15-16.6)^2 + (19-16.6)^2 = 31.8 Medication 3: SS = (14-14.4)^2 + (17-14.4)^2 + (20-14.4)^2 + (15-14.4)^2 + (0-14.4)^2 = 30.4
Step 3: Calculate the total sum of squares (SST): SST = SS for Medication 1 + SS for Medication 2 + SS for Medication 3 = 12 + 31.8 + 30.4 = 74.2
Step 4: Calculate the mean square (MS) for each medication: MS = SS/df where df = number of treatments – 1 = 2 MS = 74.2/2 = 37.1
Step 5: Calculate the F-statistic: F = MS for treatment / MS for error MS for error = SSE/df where df = n – number of treatments n = number of observations in each medication df for error = 5 – 3 = 2 SSE = SST – SS for treatment = 74.2 – 37.1 = 37.1 MS for error = SSE/df = 37.1/2 = 18.55 F = MS for treatment / MS for error = 37.1 / 18.55 = 1.99
Step 6: Compare the F-statistic to the critical value: At α = 0.01 and df = 2, the critical value from the F-distribution table is 6.635. Since F = 1.99 < 6.635, we fail to reject the null hypothesis.
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