86 Milton Landowne 



shows a scatter plot of the individual values. The coefficient 

 of variability was db 32 per cent. About half of the total 

 variance, or one-third of the standard deviation, turns out to 

 be associated with difference in age. A decline in cardiac output 

 is evident after the third decade, and, on the average, there is 

 a decrease in cardiac output of 1 per cent of the 50-year 

 value per year.* 



Table I 



Parameters of regression equations based on the formula: 



y = y6oe (b±S.E. b ) X 



WHERE y fi0 = PREDICTED 50-YEAR VALUE ; b = PERCENT CHANGE PER YEAR; 

 S.E.b = STANDARD ERROR OF b, X ~ AGE MINUS 50 YEARS. 



The 1 per cent decrease in cardiac output per year may be 

 seen (Table I) to be due in most part to a decline in cardiac 



* In Figs. 6 and 7, the line represents a simple linear regression equation 

 with a slope that is significantly different from zero. The equation y = a + bx, 

 and the standard error of the slope b is a conventional and convenient way of 

 expressing results. The assessment of relative contributions of several variables 

 may be furthered by using partial regression statistics. Slight modification 

 of this representation is even more appropriate to these agewise studies. 

 The linear regression equations fitted to the natural logarithm of values 

 for cardiac output, etc., furnishes an equation of the form y = aebx. The 

 fit has been generally improved by this, and that technically justifies the 

 procedure, but we do not suppose that this actually represents the true regres- 

 sion pattern. The second equation possesses the truly added advantage of 

 providing a series of dimensionally consistent expressions, for "b" is now the 

 fractional change per year. When "x" = age in years, "a" becomes the pre- 

 dicted value at zero years of age which is a relatively useless bit of information. 

 But by making "x" equal to the difference between age and 50 years, "a" 

 becomes the predicted 50-year value. This is more informative than is the mean 

 of the sample, and serves as a mild emphasis to give the older individual his due. 



