BIOMETRICS i6i 



height, 69 inches. We can now measure the slope of the 

 Hne AB mathematically by the tangent of the angle AOE. 

 If this angle is 45 degrees — i.e., if AB fall on CD, its value 

 tan<:['AOE= i ; if the angle is o degree — i.e., if AB fall 

 on EF, its value = o. The correlation varies therefore 

 between i and o, and is the greater the nearer it is to i. 

 In our case the slope would be expressed by J or o- 5 . This 

 is called the " Coefficient of Correlation," or r, and gives 

 us the measure of correlation between the heights of the 

 fathers and that of their sons. 



Now, what does this mean exactly ? We have seen that 

 the heights of the fathers are represented in our diagram 

 by CD, that of the corresponding arrays of sons (taking 

 each time the mean of the array) by AB, and the height of 

 the average population by EF = 69 inches. We learn 

 from the diagram that when the father is 62 inches high 

 the son is on an average 65-5 inches ; while the father is 

 7 inches below the average of 69 inches, the son is only 

 3-5 inches below it — i.e., only half that amount. When the 

 father is 75 inches high, or 6 inches above the average, the 

 son will be on an average only 72 inches — i.e., only 3 inches 

 above the average, again half of the father's amount. The 

 same holds good for any given class of fathers and their cor- 

 related sons. In other words, the deviation of the son from 

 the mean height of the population (P) is half the amount 

 of the deviation of the father from P. If P is the mean 

 height of the population, and D is the deviation of the 

 father from P, then P±D expresses the height of the 

 father (4- if he is above the average, — if he is below it), 

 while the average height of his sons would be P± JD. In 

 short, we find the son deviates less from the mean of the 

 population than does the father ; or, in other words, the 

 son regresses from the father towards the mean of the 

 population. 



We see, then, that Correlation and Regression are the 

 same, but viewed from different standpoints. While cor- 

 relation expresses by how much the son resembles his 



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