The stature of men may be said to vary usually between limits of 62 and 76 inches, the average height being about 69 inches. In the complete absence of heredity in stature we should find that fathers of any given height, say 62 or 63 or 76 inches would have sons of no particular height but of all heights with an average of 69 inches, the same as in the whole group. Or if stature were completely heritable from one generation to the next the _total generations being the units compared_, then 62 or 63 or 76 inch fathers would have respectively sons all 62, 63, and 76 inches tall. When we examine the actual details of the resemblance we find, as a matter of fact, that neither of these possibilities is actually realized. What we do find is that fathers below or above the average height have sons whose average height is also below or above the general average but not so far below or above the general average as were the fathers. If we measured a large number of pairs of fathers and sons with respect to stature we should find each generation with a variability such as that illustrated in Fig. 3 of the stature of mothers, the limits here, however, being about 62 and 76 inches. But if we measured all the sons of 62-inch fathers they would be found to vary say from 62 to only 69 inches, averaging about 66 inches. Similarly 63-inch fathers would have sons from 62 to 70 inches tall, averaging about 66.5 inches, or 76-inch fathers might have sons from 69 to 76 inches in height, averaging about 72 inches, and so on for fathers of all heights. In general, then, we may say that fathers with a characteristic of a certain plus or minus deviation from the average of the whole group have sons who on the whole deviate in the same direction but less widely than the fathers, although the fact of variability comes in so that some few of the sons deviate as widely as, or even more widely than, the fathers, others deviate less widely than the fathers from the average of the whole group. This is the general and very important statistical fact of _regression_.