90 MASS. EXPERIMENT STATION BULLETIN 251 



sion in the preceding section of the principal variables and their relation 

 to labor return per bird connpletes the picture of the significance of each 

 of the factors. 



Other Factors and Unexplained Variation 



It will be of interest to refer to the total variation in labor return per 

 bird and see how much of it has been accounted for by the factors which 

 have been considered. In 1927 the variation in labor return per bird 

 was from $ .66 to $11.52. The labor returns per bird estimated from the 

 regressions varied from $0.18 to $8.04. The fact that the regression 

 formula gave estimated values for labor return per bird, half of which 

 fell within a range of about 78 cents either way from the actual labor 

 return, indicates the degree of reliability of the study as a whole. This 

 is fairly good, but since the multiple correlation was by no means per- 

 fect, (leaving 32.9 per cent of the squared variation unaccoimted for), other 

 factors not studied must have had considerable influence. A small part of 

 the variation is always due to errors in the collection of the data, but 

 in this case it seems probable that variations in cost factors, particularly 

 feed, may account for a large part of the remaining differences. 



In order to test the truth of this assumption an analysis was made of 

 the relationship between costs and the unexplained or residual variation 

 for the 1927 records.^ The correlation between the residuals and total 

 costs was found to be r=: .28. It appeared from dot charts that this was 

 about as much as would be found between feed costs and the residuals. 

 A correlation coefficient of r^ .28, although not high, has some significance 

 and shows that costs did account for a part of the dift'erences not ex- 

 plained. Using the regression from the correlation as a correction formula, 

 new estimates were made, and new residuals computed to determine how 

 much closer the average estimate was. The probable error of estimate 

 was cut down from 78 cents to 65 cents and the average deviation of the 

 residuals was changed from 76 cents to 71 cents. 



^ Residuals were computed by first estimating labor returns from the regression 

 equation and then subtracting the estimates from the actual labor returns. 



