468 TRANSMISSION 



predict what will probably be the deviation of the correlated char- 

 acter from its mean. Thus, suppose we select ears which deviate, 

 say two inches, from the mean length of ears ; that is, which are 

 two inches above the average : the regression coefficient (2.03) 

 of weight relative to length indicates that we should expect such 

 ears to be about 4.06 ounces from the mean, that is 2 X 2.03. 

 To be more general, if we select ears which have any deviation 

 x from the mean length, we should expect their deviations in 

 weight to center about a value 2.03 x from the mean weight of 

 ears for the whole population. 



The regression coefficient is thus a fixed ratio between devia- 

 tions of correlated characters, so that, knowing how much one of 

 the characters differs from its mean in any unit of measurement, 

 say inches, we are enabled to predict how much the associated 

 character departs from its mean in its unit of measurement, say 

 in pounds. Thus if a regression coefficient of weight upon stat- 

 ure is, say 2.17, we know that any departure from the mean 

 stature will be followed by a departure 2.17 times as great in 

 respect to weight, using in both cases the same units as were 

 used in calculating the coefficient ; for example, feet and pounds, 

 inches and ounces, or even inches and pounds, if these were the 

 units actually used in computing the regression coefficient. 



SECTION VI STUDIES IN SPEED RECORDS OF 

 TROTTERS 



Studies were made of 13,879 trotters possessing records of 

 2 : 30 or better, in order to learn their distribution as to speed, 

 and the possible correlation of speed with color, and more par- 

 ticularly with sex (see tables, pages 469 and 470). 



The data were taken for each quarter second, and the record 

 made a scroll over forty feet long. The matter is here con- 

 densed to differences of one second in order to bring it into 

 suitable space. 



The original record showed two strange peculiarities. Almost 

 invariably the largest number of records was found on the first 

 quarter second after the even minute, as 20^, 21^, etc. ; that is 

 to say, the records were not evenly spread, or, as mathematicians 



