Question

5.52. Potency of a drug. Eli Lilly and Company has developed three methods (G, R1, and R2) for esti- mating the shelf life of its drug products based on potency. One way to compare the three methods is to build a regression model for the dependent variable, estimated shelf life y (as a percentage of true shelf life), with potency of the drug (x1) as a quantitative predictor and method as a qualitative predictor.

(a) Write a first-order, main effects model for E(y) as a function of potency (x1) and method. SAS Output for Exercise 5.51

(b) Interpret the β coefficients of the model, part a.

(c) Write a first-order model for E(y) that will allow the slopes to differ for the three methods.

(d) Refer to part c. For each method, write the slope of the y – x1 line in terms of the β’s.

Answer 1

Multiple Regression Analysis:

Here consider a regression model,based on n observations,with k independent variable

and the dependent variable Y,is shown below

So the estimates of the model parameters are computed using the least squares of errors method.

The % confidence interval for the point estimate of the coefficient of jth independent variable, is given by the formula .Here the has degrres of freedom

a) Inorder to predict the shelf life of the drug products y based on their potency and the methods used to estimate the shelf life the first order main effects model can be written as:

b) Now let us interpret the model defined in part d)

c) We are now interested in stating the first order model that will allow the slopes to differ for the three methods.The proposed model is:

Since the interaction terms are involved,the slopes will differ for three months

d) Let us write the slopes y on x_i line for each method in terms of defined in the model in part c)