Sir Francis Galton, a Cousin of James Darwin, Examined the Relationship

Essay

Sir Francis Galton, a cousin of James Darwin, examined the relationship between the
height of children and their parents towards the end of the 19th century.It is from this
study that the name "regression" originated.You decide to update his findings by
collecting data from 110 college students, and estimate the following relationship: $$\widehat { \text { Studenth } } = 19.6 + 0.73 \times \text { Midparh, } R ^ { 2 } = 0.45 , S E R = 2.0$$ where Studenth is the height of students in inches, and Midparh is the average of the
parental heights.(Following Galton's methodology, both variables were adjusted so that
the average female height was equal to the average male height.)
(a)Interpret the estimated coefficients.