Refer to the Drug Development and Industrial Pharmacy (Vol. 28, 2002.) investigation of the rate at which a drug is released in a controlled-release dosage, Exercise 10.26. Recall that the ratio of surface area to volume and the diffusional release rate (percentage of drug released divided by the square root of time) was measured for each of six drug tablets. The experimental data are reproduced in the table. Use matrix algebra and the method of least–squares to fit the straight-line model E(y) = β_o + β₁x to the six data points.

a. Construct Y and X matrices for the data.

b. Find X'X and X'Y.

c. Verify that

d. Find the b matrix, then give the least-squares prediction equation.

e. Find SSE and s².

f. Find the standard error of β̂₁.

g. Test H_o: β₁ = 0 against H_a: β₁ ≠ 0,using α = .05.

h. Find and interpret the value of R².

i. Give and interpret a 95% confidence interval for E(y) when x = 1.

Data from Exercise 10.26

Researchers at Dow Chemical Co. investigated the effect of tablet surface area and volume on the rate at which a drug is released in a controlled- release dosage. (Drug Development and Industrial Pharmacy, Vol. 28, 2002.) Six similarly shaped tablets were prepared with different weights and thicknesses and the ratio of surface area to volume was measured for each.

Transcribed Image Text:

DOWDRUG Drug Release Rate, y (% released/V time) Surface Area to Volume, x (mm?/mm) 60 1.50 48 1.05 39 90 33 .75 30 .60 29 .65