Project #2
STAT 450/870
Fall 2015
Complete the following problems below as a continuation of the shelf life problem from Project #1.
Within each part, include your R program output with code inside of it and any additional information needed to explain your answer. Your R code and output should be formatted in the same manner as in the lecture notes. Use

=0.05 for all inference procedures where needed.
1) (23 total points) The purpose of this problem is for you to get experience with the diagnostic and remedial measures described in Chapter 3. Continue to use the population regression model of
E(Potency) =

0
+

1

Time unless otherwise indicated. a) (5 points) Using my examine.mod.simple() function, comment on the following items with regards to the model: i) Linearity of the regression function ii) Constant error variance iii) Normality of
 i iv) Outliers
Make sure to specifically refer to plots in your comments. b) (4 points) Below is how I actually simulated the data set:
set.seed(9192)
time<-c(3,6,9,12,15,18,21,24,30,36,48,60)
epsilon<-rnorm(n = length(time), mean = 0, sd = 0.014)
beta0<-1
beta1<--0.001
potency<-beta0 + beta1*time + epsilon
set1<-data.frame(time, potency)
set1
Based on this code only, discuss the four items listed in part a). c) (5 points)
Suppose the “ potency<-beta0 + beta1*time + epsilon ” line of code in part b) was changed to potency<-beta0 + beta1*time - 0.0001*time^2 + epsilon
Run the code in b) with the above changes, estimate the E(Potency) =

0
+

1

Time model again
(without time 2 ), and re-run my examine.mod.simple() function. Using the output from examine.mod.simple() , what has changed with respect the four items listed in part a). d) (5 points) What could you change in the code of part b) so that there is not constant variance?
Implement this change in the code, estimate the E(Potency) =

0
+

1

Time model again, and re-run my examine.mod.simple() function. Using the output from examine.mod.simple() , what has changed with respect to the four items listed in part a). e) (2 points) What could you change in the code of part b) so that the normality assumption does not hold? Note that you do not have to implement the change.
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f) (2 points) What could you change in the code of part b) so that there is one outlier? Note that you do not have to implement the change.
2) (13 total points) The purpose of this problem is to apply the procedures given in Section 4.6 to find the shelf life in an alternative manner to what the FDA requires. Suppose the sample regression model to estimate E(Potency) =

0
+

1 time is being used throughout this problem. a) (2 points) What is the estimated time value when potency is 0.95? b) (4 points) Find the approximate confidence interval for the true value of time when potency is
0.95 and interpret the interval in the context of the problem. c) (3 points) Add appropriate graphical representations of the numerical values in parts a) and b) to your plot constructed in project #1. d) (4 points) Using inverse prediction, there are two possible choices for an expiration date: i) The answer to part a) ii) The lower bound to part b)
Which of these choices would be more statistically correct to use? Explain your answer.
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