io6 INHERITANCE IN ANIMALS 



is what Mr. Galton has called the ' Regression ' of second 

 results on first results. We may express the facts illus- 

 trated by the line of circles on our diagram by saying that 

 the regression of second throws on first throws is |. If 

 you examine the line of crosses as we have examined the 

 line of circles, you will easily see that the regression of 

 first throws upon second throws is also \. 



If we had made our second result depend entirely upon 

 the first, if we had carried all twelve dice unchanged from 

 the first result into the second, simply counting them 

 over again, without tossing them at all, the two results of 

 each pair would have been identical, and if we tried to 

 indicate that on such a diagram as fig. i, we should have 

 to make the circles and the crosses of that diagram all lie 

 on one straight line, inclined to the axes at an angle of 45. 

 The regression of either set of results upon the other 

 would then be unity. If, on the other hand, both results 

 had been entirely independent, the line of circles would 

 become horizontal, the line of crosses vertical, and the 

 regression of either first or second results upon the other 

 would be zero. 



I have been anxious to show you this phenomenon of 

 regression first of all in an experiment with dice, because 

 you see more clearly from such an experiment, the way in 

 which it is brought about. You see that we are obliged 

 to express the relation between our correlated sets of 

 results with dice in terms of this kind, because when we 

 know the result of a first throw, we know some of the 

 elements which determine a second throw, but not all of 

 them. There is nothing peculiarly vital in this phenome- 

 non of regression, and I have been anxious to make that 

 point clear to you, because it is not generally understood. 

 The term Regression was introduced into biological work 

 by Mr. Galton, in his discussion of the relation between the 

 stature of human parents and the stature of their children. 



