Multiple linear regression analysis scintillation gamma-ray spectra: Theoretical and practical considerations

Abstract

Application of the method of multiple linear regression (MLR) as a data-analysis technique for gamma-ray scintillation spectrometer data requires knowledge of (1) the response matrix of the spectrometer and (2) the covariance matrix of the unknown spectrum (or spectra). Neither matrix is known exactly. The response matrix can usually be determined with good precision and an estimate of the covariance matrix can usually be made. Perturbation or errors in either matrix, however, will introduce biases in the results. In addition, in the formulation of the method, assumptions are made and criteria are specified which may be appropriate for particular applications. Once generated, the particular formulation is frequently assumed to be generally applicable; additional biases can thereby be introduced. In this report, theoretical and practical considerations are delineated which are important to the satisfactory utilization of the MLR method. Subjective judgments which are introduced in the formulation of the method are indicated, and in view of these judgements, specific areas are described where care must be exercised, both in the acquisition of the data and in the subsequent processing.