CORRELATION AS APPLIED TO FARM-SURVEY DATA. 11 



the statement already made that the price was generally higher later 

 in the season. The remaining gross coefficients are -|-.01 for total 

 value of feed consumed per head and cost at weaning time, +.42 for 

 value of feed consumed and date of sale, and —.04 for cost at wean- 

 ing time and date of sale. The coefficients -]-.01 and —.04 show that 

 cost at weaning time is uncorrelated with either value of feed con- 

 sumed or date of sale. With regard to the correlation between value 

 of feed consumed per head and date of sale, we may say that the 

 value of feed consumed is probably very nearly proportional to the 

 length of the feeding period, and if the actual length of time on feed 

 had been used hei'e instead of its approximate measure, the date 

 of sale, the correlation would probably have been higher. 



EFFECT OF THE OTHER FACTORS ON THE APPARENT CORRELATIONS. 



The small degree of correlation present between profit and weight 

 is mostly due to differences in price, the coefficient being reduced 

 from +.28 to +.18, when the value per hundredweight is taken into 

 account ; that is to say, the tendency of the heavier calves to be the 

 more profitable is mostly due to the fact that they sold for a better 

 price per pound than that commanded by the smaller calves. 



The coefficient r^^j is 4--50, which is considerably higher than the 

 gross coefficient, showing that if the value of feed had been constant 

 while other things remained unchanged, the correlation between 

 profit and weight would have been greater. 



The correct explanation of the size of the coefficient rjyi„,c, which 

 is +.48, is not so apparent. It indicates, however, that if the in- 

 fluence of the cost at weaning time, the factor most closely related to 

 profit, were eliminated, the correlation between profit and weight 

 would be greater. 



When the date of sale is taken into account, the correlation be- 

 tween profit and weight becomes somewhat less than the gross cor- 

 relation, but the difference is not enough to be significant. 



The coefficients obtained for the correlation between weight and 

 profit, when the effect of the other factors, two at a time, is con- 

 sidered, are generally higher than when they are considered one at 

 a time. This means that if the influence of two of the factors con- 

 tributing to the profit or loss is eliminated, its correlation with any 

 of the remaining factors is higher than if the influence of but one 

 had been eliminated. 



It is interesting to note here that the correlation between weight 

 and profit, even when the other factors are taken into account, is 

 almost entirely independent of the date of sale. The apparent cor- 

 relation, +.28, becomes +.24 when date of sale is taken into ac- 

 count. When value per pound is taken into account, the coefficient 

 is +.18 ; when price and date of sale are considered simultaneously, 



