This paper shows that (1) the principle of substitution has been misinterpreted in regression analysis on residential homes by the misuse of the confidence interval; (2) the proper confidence interval to judge the accuracy of the equation is the mean CI; and (3) the accuracy of the equation can be improved by applying factor analysis to theentiredata set rather than apredeterminedneighborhood. These results are illustrated in a sample of 571 residential sales in Northwest Arkansas during 1975. The data are divided into clusters, and a regression equation is computed for each. The results show that the mean confidence interval is the correct application of the principle of substitution. The correct decision rule to determine the superiority of the multi‐equation or the single equation model compares the explained to the unexplained variation. These results should allow the appraiser to select properties that are better suited for comparison. This will improve the accuracy of the regression analysis and resulting estimates of property valu