A slope of 1 would be perfect correlation, which means every extra inch for the father is passed deterministically to the son, who would also be an inch taller. The slope can never be greater than 1; if it were, the sons of tall fathers would be taller on average, and the sons of short fathers would be shorter—and this would force the distribution of heights to become wider over time. After a few generations we would start having 9-foot people and 2-foot people, which is not observed in nature. So, provided the distribution of heights stays the same from one generation to the next, the slope
...more
