Statistical Procedures for Predicting Length Characteristics of Top from Raw Wool Measurements

Abstract

This paper deals with the application of regression procedures and cross-validation for predicting the resultant fiber-length characteristics of tops from raw wool measurements. Alternative methods of choosing raw wool variables and then estimating regression coefficients for prediction are compared. Data from 39 commercial batches from a single mill are used for this evaluation. The statistical problems associated with prediction are discussed; however, further mill studies will be required to assess the potential of the predictive relationship obtained in this study.Prediction of fiber length of top remains a major problem for the topmaker or comber. While there has been a steady increase in the use of raw wool measurement for a number of other processing factors, there is still a large subjective component involved in batching wools to meet the fiber-length specifications for tops. Difficulties facing topmakers in this respect are outlined by Bell [3], and research in this field has a high priority.Studies over the years have demonstrated how the length during and after processing is influenced by raw wool characteristics. In two recent studies [9,14], batches of wool were monitored for a selection of measured raw wool characteristics to examine their relative influence on the fiber length of tops and on other processing factors. Statistical procedures were used to determine the degree of association between the processing factors and the raw wool measurements. High levels of association were found between selected subsets of the characteristics of greasy wool and many of the processing factors. For example, in the study on 39 batches from a commercial combing plant [9], over 96% of the variation in the batches, for hauteur, was accounted for by subsets of raw wool measurements, including mean fiber diameter, staple length, and staple strength.Bear in mind, however, the distinction between the objectives of such studies: explanation, the screening of the variables to determine which has a significant effect on the response, or prediction, arriving at the most effective equation for predicting future observations [7]. In the studies above the emphasis was placed on the explanation of processing performance in terms of the important raw wool variables, rather than prediction. This paper extends the analyses by examining the predictive ability of alternative approaches to the data of the earlier work [9]. Specifically, we compare four methods of choosing subsets of raw wool variables and then estimating regression coefficients for the prediction equations. Statistical AspectsThe objective is to predict the fiber-length parameters of the top using regressions on variables that are derived from the raw wool measurements. In statistical terms, the length parameters of the top are the dependent variables, and the raw wool measurements, or derivatives of such, are referred to as either the predictor or explanatory variables (terms) according to the circumstances. The populations of mill batches are referred to as the ...