Expiration dates that establish the shelf lives of pharmaceutical products are determined from stability data in drug formulation studies. In order to measure the rate of decomposition of a particular drug, it is stored under various conditions of temperature, humidity, light intensity, etc., and assayed for intact drug potency at FDA-recommended time intervals of every three months during the first year. In this example, the assay Y (mg) of a certain 500 mg tablet formulation is determined at time X (months) under ambient storage conditions.
X 0 3 6 9 12
Y 500 490 470 430 350
(a) Graph these data points (xi , yi) in a scatterplot, and calculate the sample correlation coefficient r=Sxy/Sx.Sy. Classify the correlation as positive or negative, and as weak, moderate, or strong.
(b) Determine the equation of the least-squares regression line for these data points, and include a 95% confidence interval for the slope β1.
(c) Sketch a graph of this line on the same set of axes as part (a); also calculate and plot the fitted response values y, and the residuals ei= yi - ŷi, on this graph.
(d) Complete an ANOVA table for this linear regression, including the F-ratio and corresponding p-value.