On the Coefficient of Determination Ratio for Detecting Influential Outliers in Linear Regression Analysis

Abstract

The initial procedure of the Coefficient of Determination Ratio (CDR) for determining outliers in linear regression model is suggested for centred data and declares an observation as an outlier if the CDR value deviates from unity. Although the method performs very well and detects more precisely the requisite outliers than those observed by other well-known detection measures, the cut-off rule approach is a source of subjectivity and the data structure for which the method is designed is also restrictive. In this study therefore, a more rigorous cut-off rule of the same method for identifying influential observations is outlined for an updated method of the CDR that covers the more general case of a non-centred data. A cut-off rule is specified that involves the ratio of quantile values of the Beta distribution. An automated implementation of the procedure is presented that makes use of datasets in the literature and those that are simulated under various conditions of sample size, number and distribution of explanatory variables. The method is now made more generalized in application, objective and reliable as a detection measure than the initial proposal. It therefore provides most appreciable improvement in the explanatory power of linear regression models when the identified outliers are deleted from the data.