Potency of an Antibiotic An experiment was conducted to observe the effect of an increase in temperature on the potency of an antibiotic. Three 1-ounce portions of the antibiotic were stored for equal lengths of time at each of these temperatures: 30°, 50°, 70°, and 90°. The potency readings observed at each temperature of the experimental period are listed here:
Potency Readings, y
38, 43, 29
32, 26, 33
19, 27, 23
14, 19, 21
Use an appropriate computer program to answer these questions:
a. Find the least-squares line appropriate for these data.
b. Plot the points and graph the line as a check on your calculations.
c. Construct the ANOVA table for linear regression.
d. If they are available, examine the diagnostic plots to check the validity of the regression assumptions.
e. Estimate the change in potency for a 1-unit change in temperature. Use a 95% confidence interval.
f. Estimate the average potency corresponding to a temperature of 50°. Use a 95% confidence interval.
g. Suppose that a batch of the antibiotic was stored at 50° for the same length of time as the experimental period. Predict the potency of the batch at the end of the storage period. Use a 95% prediction interval.