16 A BIOMETRIC STUDY OF BASAL METABOLISM IN MAN. 



The practical physiological significance of this statistically well- 

 known relationship seems to be rather great. 



First of all, if r xh be small the error of prediction of the heat-pro- 

 duction, h, of a single individual from the value of x will necessarily 

 be large. This is not due to any inadequacy of the statistical formulas, 

 but is the inevitable consequence of great physiological variability. 



On the other hand, if there be a group of n individuals of a specified 

 grade of x, say x p , the prediction of the average heat-production of the 

 individuals of this group can be carried out with far greater accuracy. 

 Thus the standard deviation of the predicted mean value h Xp is 



-r xh 2 



Vn 

 while the probable error is 



0.67449 ff h Vl -r xh 2 

 Vn 



where h x is the mean heat-production of individuals of a specific 

 grade, p, of character x, for example body-weight, body-surface, pulse- 

 rate, or any other character. 



Thus it is clear that when a physical character of an individual is 

 known for example, stature or body-weight the values of metabol- 

 ism predicted from it will show certain deviations from the actual 

 values of the individual subjects, but the statistician can even predict 

 with fair accuracy what the amount of this deviation will be. The 

 failure to attain exact prediction merely illustrates the fact that physi- 

 ology, like biology in general, is not as yet a science in which certainty 

 as to the individual instance is attainable. Chapter VI will be devoted 

 almost entirely to the problem of the closeness of prediction of heat- 

 production from physical characters. 



As an illustration of the importance of the preceding formulas we 

 may note that the probable error of the mean predicted heat-production 

 of 4 typhoid patients would be 1/V 4 or one-half as large as the probable 

 error of a single individual, while the probable error_of the mean pre- 

 dicted heat-production of 9 subjects would be 1/V9, or one-third as 

 large as the probable error of one observation. 



To determine how closely the predicted values agree with the empir- 

 ical average for the group of individuals classified with respect to any 

 character, x, we have merely to compare the mean values actually 

 observed with those due to the regression equation by means of a 

 graph. Such diagrams, of which a number occur in the following pages, 

 permit one to judge by the eye the goodness of fit of the regression 

 equations. In some cases special mathematical tests of the closeness 

 of agreement of the empirical and theoretical means are given, but an 

 explanation of the nature of these tests is unnecessary here. 



