The effect of tablet surface area and volume on the rate at which a drug is released in a controlled-release dosage is of interest to chemical companies. In one study, six similarly shaped tablets were prepared with different weights and thicknesses, and the ratio of surface area to volume was measured for each. Using a dissolution apparatus, each tablet was placed in 900 milliliters of deionized water, and the diffusional drug release rate (percentage of drug released divided by the square root of time) was determined. The experimental data are listed in the table (next column).

a. Fit the simple linear model, E(y) = β0 + b1x, where y = release rate and x = surface-area-to-volume ratio.

b. Interpret the estimates of β0 and β1.

c. Find the value of s for the straight-line model.

d. Give a practical interpretation of the value of s.

e. Form a 90% confidence interval for the slope, β1. Interpret the result.

f. Predict the drug release rate for a tablet that has a surface area/volume ratio of .50. Support your answer with a 90% prediction interval.

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Drug Release Rate (% released/Vtime) Surface Area to Volume (mm²/mm³) 1.30 0.85 0.70 0.55 0.40 0.45 40 32 26 22 20 19