Correlation and Simultaneous Linear Regression

Hirschfled (1935) posed the question. Is it always possible to introduce new variates for the rows and the columns of the contingency-table such that both regressions are linear. In reply, he derived the formulas of dual sealing. This approach was later employed by Lingoes (1963, 1968) who was obviously unaware of Hirschfeld’s study, but noted that the approach would use the basic theory and equation worked out by Guttman (1941). We have to use a graphic with linear regression to find optimal weight which has good results by using a correlation as a new step to adjusting the spacing of rows and columns after quantification is linear, the condition under which correlation attains its maximum. It shall present here merely an example to illustrate the date have a certain ρ = 0.65277 between x and y which increases to reach the maximum value then the relation becomes a straight line which illustrates the maximum value of ρ.