90 MANUAL OF DAIRY CATTLE BREEDING 



The value of a y is equal to the square root of a 2 y or ->Jl9 .559267 = 4.422586 

 The value of the correlation coefficient is equal to 



S(XY) _ S(X) S(Y) 



4.111300 n „ nnnn .. , , n n n 



or 0.412227 or in symbols 



2.255104X4.422586 ax X ay 



The class interval, between 1 and 2 for instance of the X is equal 

 to 1000 pounds of milk. The origin, on the A" scale, is equal to 

 3500 pounds of milk. In the same way the class interval for Y is 

 equal to 0.5 of a year and the origin is equal to 1.25. From 

 these data the mean average milk yield and age at test is found to 

 be: 



5.755167 X 1000 + 3500 = 9255 pounds of milk 

 6.124577 X 0.5 + 1.25 = 4.31 years of age 



The standard deviations for milk yield and age are equal to the a 

 times the class interval, or : 



o-x X 1000 or 2.55104 X 1000 = 2255 pounds 

 o-t X 0.5 or 4.422586 X 0.5 = 2.21 years 



There are two possible linear equations for this correlation table, 

 one to give the mean milk yields when the age is known and the 

 other to give the mean ages when the milk yields are given. The 

 equations are equal to: 



99^£ 9955 



Mean milk yield = 9255 - 0.412 —^ 4.31 + 0.412 ^~ age, 



or mean milk yield = 7443 + 420.4 age. 



2.21 2.21 



Mean age = 4.31 - 0.412 rr — 9255 + 0.412 rr— milk yield, 

 ZZoo ZZoo 



or mean age = 0.61 + 0.0004 milk yield. 

 In symbols, the equations are: 



S.D. X S.D. X 



X = mean x - r XY g -^ mean Y + r XY g -p. Y 



O.JJ.y b.D.Y 



S.D. Y S.D. Y 



Y = mean Y - r XY -^ mean x + r XY a 



b.JJ.x b.JJ.x 



where S.D. is equal to the standard deviation. 



