58 Maine Agricultural Experiment Station. 1920. 



higher than the correlation coefficient. This difference is shown 

 to be highly significant by the value of -q — r -j-0.1689zt.0201. 

 It is altogether probable therefore that the regression of age 

 on milk production is a skew regression. This is shown to be 

 a fact by the constant to measure such skewness. -q - — r M 

 o.n6izt.oio8 is about 11 times its probable error. The re- 

 gression is therefore known to be skew. Since this is true the 

 correlation ratio is a better measure of the true correlation 

 than is the correlation, coefficient. The relation of age at test 

 is then doubly significant in any comparison of the records of 

 two cows. The regression having been shown to be skew it 

 becomes necessary to deal with it separately. 



Type of the Regression of Milk Production ox Age of 

 Jersey Cattle. 



The means for each array of age have been calculated. 



From these means the theoretical' curve conforming to the 

 general logarithmic type has been calculated by the method of 

 least squares. The equation to this curve is 



3— 338/-9 I2 ^9- 8 83' 1 '— 48/^ 2 +2896.2i9 Log x 



where x is taken in six months intervals from an origin at 1 

 year and 3 months. 



The observations at the higher ages vary a good deal as 

 they are based on small numbers. The theoretical curve strikes 

 through them quite accurately when the unevenness of the ob- 

 served curve is considered. When we calculate the x 2 by the 

 method of Slutsky we find that 5 observations contribute a sum 

 of 28.80 to the total of 45.41. These observations are at ages 

 2 years 9 months, 3 years 3 months, 6 years 9 months, 7 years 

 9 months and 9 years 3 months. If we measure the fit by the 

 total x 2 45-4 1 it is poor. Considering the above mentioned five 

 observations in connection with the other observations it is seen 

 that two of them are plus and three are minus quantities. Not 

 only that but they come at places in the curve so that they would 

 practically counteract each other if the first smoothed curve 

 were used as the observational. It seems altogether reasonable 



