466 TRANSMISSION 



before by the product of the number of variates and the two 

 standard deviations. Finally we subtract from this result the 

 products of the two corrections to our guesses in finding means, 

 after dividing that product by the product of the standard devi- 

 ations of the two systems of variates. 



We shall present on page 467 an illustration of this shorter 

 method, using for the purpose the correlation between length 

 and circumference of ears of Learning corn. In this G L and G c 

 are the guesses at the class mark nearest to the mean of the 

 population as to length and circumference respectively. 



Let M L and M c be the mean length and circumference respec- 

 tively, and C L and C c the corrections to G L and G c which give 

 M L and J/ so that M L = G L + C L and M c = G c + C c . 



Also let DL and D c ' represent deviations of class marks 

 from the guesses G L and G c respectively. 



Unless one carries through a large number of decimal places 

 the method previously discussed is not only very laborious but 

 it is much less accurate than the shorter method here described. 



SECTION V THE REGRESSION COEFFICIENT 



From the correlation coefficient and the standard deviations 

 with respect to two characters it is easy to obtain what is known 

 as the regression coefficient. To obtain the regression coefficient 

 of the weight of ears relative to their lengths, multiply the 

 coefficient of correlation by the standard deviation of weight, 

 and divide the product by the standard deviation of length. 



This gives, for the regression of weight relative to length, 



v 

 r = 2.03. 



*L 



Similarly, the regression of length relative to weight is 



r*>- 



v 



Use of the regression coefficient. The regression coefficient is 

 useful for prediction ; that is to say, if we know the deviation 

 of one character from its mean, this coefficient will enable us to 



