7.1 Jensen, Birch, and Woodall (2008) considered profile monitoring of a calibration data set in which the data consists of 22 calibration samples. One of the purposes of the experiment was to determine the relationship between an absorbance measure (absorbance) of a chemical solution to the volume at which the solution was prepared (volume). The raw data are provided in calibration.xls.

(a) Graphically investigate the relationship between absorbance and volume in a sample specific manner.

(b) Determine which model—(1) random intercept model, (2) random slope but common intercept, or (3) random intercept plus random slope model—is most appropriate for these data, shown in the following table. Use hypothesis testing with a significance level of 0.05 to make your decision.

(c) Based on the model in part (b), estimate the common variancecovariance matrix for each sample.

(d) Provide an expression for the marginal mean relationship between absorbance and volume.

(e) Provide an expression for the conditional mean relationship between absorbance and volume.