CHAPTER XIII 

 Age of the Cow in Relation to the Butter-fat Percentage 



This subject is much less complex than the same relations for 

 milk yield. The relation is, in general, a linear one with a difference 

 in the effect of age on the butter-fat percentage of the different breeds. 

 The student will find it advantageous to calculate a table show- 

 ing the raw data for the influence of age on the butter-fat percentage. 

 These data may be found in the same references as those for the 

 relation of age to milk yield. 



The method of calculation necessary to determine this relation of 

 age to butter-fat percentage may be illustrated by the table on 

 milk yield on page 78 although the linear equation is not suited 

 to describe the relation of milk yield to age. Summation X 

 (S(X)) for each row of the table is obtained as previously described, 

 S(X) of the "Total" row is also calculated (37 X 1) + (389 X 2) 



+ (1125 X 3) (1 X 17) + (1 X 21) = 61258. The sum of the 



right hand column, S(X) for each row is also equal to 61258 which 

 checks the work thus far calculated. The figure 61258 is called 

 S(X) of the table. The next constant needed is S(X 2 ). This is 

 obtained by multiplying the totals of the lower row by the squares 

 of the X row. Thus (37 X 1) + (389 X 4) + (1125 X 9) + 



(1800 X 16) + (2055 X 25) (IX 289) + (1 X 441) = 406680 



= summation X 2 , written S(X 2 ). Similar values are now obtained 

 for Y. Summation Y is equal to the totals of the right side of the 

 table times the distance from the origin shown in column F. Thus 

 S(Y) is equal to 



(244 X 1) + (2436 X 2) + (1287 X 3) + (1020 X 4) .... (1 X 31) + (1 X 33) = 



65190 



Summation Y 2 , (S(Y 2 )), is equal to the total column times the 

 squares of the distance from the origin or 



(244 X 1) + (2436 X 4) + (1287 X 9) + (1020 X 16) .... (1 X 961) + (1 X 1089) 



= 607450 



