Sir Francis Galton, a cousin of James Darwin, examined the relationship between the height of children and their parents towards the end of the 19thcentury. 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 Studenth= 19.6 + 0.73 ×Midparh, R2= 0.45, SER= 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.
(b)What is the meaning of the regression R2?
(c) What is the prediction for the height of a child whose parents have an average height of 70.06 inches?
(d)What is the interpretation of the SER here?
(e)Given the positive intercept and the fact that the slope lies between zero and one, what can you say about the height of students who have quite tall parents? Those who have quite short parents?
(f)Galton was concerned about the height of the English aristocracy and referred to the above result as "regression towards mediocrity." Can you figure out what his concern was? Why do you think that we refer to this result today as "Galton's Fallacy"?