CHANGES IN METABOLISM WITH AGE. 



117 



tion coefficients between age and heat-production for constant stature, 

 ,r ah , and between age and heat-production for constant body-weight, 

 w r ah , and finally the partial correlation between age and heat-production 

 for both stature and weight constant, i.e., sw r ah . 



These express the interrelationships between age and heat produc- 

 tion, correction being made for stature, for weight, and for stature and 

 weight, on a relative scale. To obtain the actual smoothed change in 

 metabolism per year with correction for the influence of stature and 

 weight we have merely to determine the partial regressions, p, i.e., 



tPah, v>Pah, twPa\. 



The needful regression slopes in calories per 24 hours are given by : 



O i = T i ' 



wian w' an 



where the partial correlations are already known (table 40) and the 

 partial standard deviations are given by : 



-r s 2 Vl 



7- , 2_ 



s 1 ah 



- T . 2 



..T 2 



- u r^ 



-r au , 2 Vl - w r at ?=v a Vl -r ah * Vl - 



The results for the larger series are set forth in table 41. Here the 

 second column gives the decrease in heat-production per year in the 



TABLE 41. Regression and partial regression of heat-production on age. 



several series. These are merely repeated from the list of equations 

 on page 114. The three following columns give the smoothed annual 

 decrements in heat-production corrected for the influence of stature, 

 of weight, and of stature and weight. The entries in the two final 

 columns are certainly much more uniform than those in the first two. 

 Correction for body-weight and for stature and weight have greatly 

 reduced the irregularities which are evident in the gross regressions 

 or in the regressions corrected for stature only. 



