186 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN. 



body-weight gives a slightly larger average error than prediction from 

 body-surface by the Du Bois height-weight chart when prediction 

 from body-surface is made by considering that the heat-production of 

 an individual is given by 



"D 



where a D is the superficial area of the individual by the Du Bois height- 

 weight chart and h D the average heat-production per square meter in 

 the standard population. In two cases, VI and VII, it gives a smaller 

 average deviation from the ideal zero error. 



When the best measure of heat-production on the basis of a single 

 physical measurement is supposed to be given by 



as we have demonstrated to be the case, the multiple regression equa- 

 tion gives slightly higher error in three of the four larger series. 



The difference between the results of predicting heat-production 

 by the use of multiple regression equations involving stature and 

 weight and those due to the use of linear equations for prediction 

 from body-surface by the Du Bois height-weight chart is, however, 

 very slight indeed. In only 1 of the 8 comparisons is the difference 

 over 7 calories. The difference in the percentage value of the average 

 deviations with regard to sign of the two methods of prediction is in only 

 1 case over 0.5 per cent in the 8 comparisons based on larger series. 



When the values of the individual subjects are computed from 

 equations based on the entire material for each sex (136 men and 103 

 women, as given in the two lower rows of the table) the average devia- 

 tion with regard to sign is theoretically 0, and for all practical purposes 

 empirically in our actual observational data. As far as this criterion 

 can show, all three regression methods seem equally good when predic- 

 tions of individual values are made from the constants of the population 

 to which they belong. Therefore, either of these three methods neces- 

 sarily gives better results as measured by this criterion than either of 

 the two methods of calculation from average heat-production per unit 

 of weight or per unit of body-surface area in the standard series. 



Turning now to the average deviations without regard to sign, as 

 shown in table 71, we note practically the same relationship between 

 the results for the 3 sets of formulas as in the preceding comparisons. 

 Confining our attention to the 4 larger groups (IV-VII), in which 

 prediction is made from the constants of another series of individuals, 

 we note that in 5 of the 8 comparisons the multiple prediction equation 

 shows (as indicated by the positive sign) a slightly larger, but only 

 slightly larger, error than prediction from body-surface. The difference 

 is in no case as much as 4.5 calories. In percentages of the average 



