DETERMINATION OF DIGESTIBILITY CO-EFFICIENTS             319

accuracy. The graphical method was thus brought in and as the next step, the
multiple regression equations followed as a natural corollary to it.

In order to get an idea of the nature of agreement obtained by this procedure
the case of crude protein already given as an illustration of the working out of these
methods might be taken up (Table 8, Columns 2 and 3). It will be seen that the
actually observed values of digestion (y) and the calculated or expected values
(x₁+x₂b) worked out from the value of a and b (obtained by the application of
regression equations) have recorded an unexpectedly remarkable coincidence of
agreement. The co-relation (Appendix V, Column 8) has been above 99 per
cent. and the observed ratio of variance has been much above the minimum
requirement of Fisher's 1 per cent. point of distribution. The observed and
expected values have also been plotted out (Chart 9) and it will be noted that
the variation has been negligible. For the results worked out by the graphical
method the reader is referred to Chart 4 (for protein) and Table IX. It will be seen
that by the graphical method the errors on mean (also of. Appendix III) have been
very small and the agreement between it and that of regression equations has been
reasonably close.