In this paper, using Machinery Manufacturing data as an example, the author accomplished the logical investigations of weighted correlation coefficients in Wu-Hsing Sheng-Ke (五行生剋) of business variables. The implications of correlation coefficients in three kinds of situations: specific micro-data analysis, macro-data analysis, and representative micro-data analysis, were clarified. Both individualities and their objective relative importances of micro-data were often ignored before, but they were clarified in this study. The fine connections between weighted correlation coefficients and weighted regression analysis were accomplished. Comments were also made on the inference premises of limit theorems in probability theory.