Why Two regression Lines
Once regression line cannot minimize the sum of square of deviations for both the x and Y series unless the relationship between them indicate perfect positive or negative correlation. In case of perfect correlations one regression lien is enough because X and Y series have the same type of deviations. Ordinarily in social sciences perfect correlation is very rarely found. For this reason one regression line minimizes the sum of the squares of deviations of the X series and the other regression line takes care of the deviations y series.