Problem 1.
The Food and Drug Administration (FDA) requires pharmaceutical companies to establish a shelf life for all new drug products. Pharmaceutical companies perform a stability analysis to determine how stable a drug is over time (to determine when the drug reaches unacceptable potency levels).
Regression models allow pharmaceutical companies to determine the stability of the drug and establish a shelf life. This is a very simplified case that illustrates the concept.
A pharmaceutical company wants to determine the shelf life of their new drug. A random sample of the drug in tablet form is placed into storage.
At certain time intervals (measured in months) a randomly selected tablet is taken out of storage and the potency is measured; e.g., if "Potency = 99%" then the potency of the tablet is 99% of what the company claims the drug potency to be.
Below is the sample data (problem1_data.xls is posted on Blackboard).
Time (X) Potency (Y)__
3 99.0
6 102.0
9 98.0
12 98.5
15 97.5
18 97.0
21 96.5
24 96.1
30 95.7
36 95.0
48 94.0
60 94.5
a. Create a scatter plot (time period goes on the x-axis).
Do you see a linear relationship? Paste scatter plot here.
b. Using time as the independent variable (Time period = X) and potency as the dependent variable (Potency = Y), what is the estimated regression equation (write it down)?
Paste regression output here.
c. Test the significance of the regression relationship between time and potency with α = 0.05. State (1) your hypotheses, (2) yourrejection rule, (3) the p-value, and (4) the conclusion.
d. What is the r2 for this model? What does this suggest about how well the estimated regression model fits the data? (2pts)
e. Predict the potency level for a time of 19 months.
Problem 2.
Accu-Copiers, Inc., sells and services the Accu-750 copying machines.
As part of its standard service contract, the company agrees to perform routine service on this copier.
To obtain information about the time it takes to perform routine service, Accu-Copiers has collected data for 10 service calls.
The company wishes to predict the amount of time (in minutes) it takes to perform a service based on the number of copiers being serviced (problem2_data.xls is posted on Blackboard).
Copiers (X) Minutes (Y)
4 110
2 58
5 138
7 188
1 37
3 82
4 104
5 130
2 70
4 112
a) Create a scatterplot of the data.
Do you see a linear relationship between the number of copiers serviced and the total time it took to perform the service? Paste scatter plot here.
b) Use Excel to generate regression output. What is the estimated regression equation that relates the time in minutes to the number ofcopiers serviced (write it down)? Paste regression output here.
c) Use your estimated regression equation from part (b) to predict the time to service 8 copiers.
d) Find the coefficient of determination and write it down. What does it tell you? Is this a good model?
2. The report is meant to be your reflection on the data collection process as well as a brief presentation of your findings.
Points you should address in your report:
What was your question? Is your data qualitative or quantitative? How many responses did you
obtain?
Why is the sample size important?
We are treating this as a sample from a population (and not a census). What population(s) could this sample represent?
What are your sample statistics (sample mean and standard deviation, or sample
proportions/percentages)?
Create a percent frequency distribution (i.e., list each category and the corresponding percentage;
refer to Chapter 2).
Create two graphs/charts and a confidence interval for the population mean or proportion (for qualitative data, pick one category and
create a confidence for that proportion, you do not need to create confidence intervals for each category).
Consider the information obtained from the confidence interval.
Compare it to your initial expectations.
Describe what each graph/chart is showing in the body of the report. E.g., "The pie chart in Figure 1 of the Appendix illustrates that ... is the majority opinion ..."
What issues, if any, did you run into while working with the collected data?
How did you handle them?
If you were to re-do this exercise, what would you change? Why?