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Treatment of correlation between variables is necessary for deriving any theoretical distribution of the project cost of buildings. This paper highlights some often ignored theoretical requirements necessary for a rigorous treatment of correlations. The condition for a positive definite correlation matrix is described, along with an analytical procedure and a computer program developed to verify the positive definite condition when correlation coefficients between input variables are estimated using historical data. The analytical procedure and the developed computer program can be used in any application that obtains correlation information from historical data or as subjective judgements to be used in a functional relationship. A new concept called induced correlation is suggested to define and to treat correlation between derived variables that arise from the common (shared) primary variables in their functional forms. A …