1) Sir Francis Galton, a cousin of James Darwin, examined the relationship betwe

Question

1) 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. You decide to update his findings by collecting data from 110 college students, and estimate the following relationship: (14 Points) Sudenth 19.6+0.73 x Midparh, R2-0.45 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. So we can ignore gender difference here.) (a) Interpret the estimated coefficients. (5 points) (b) What is the meaning of the regression R2? (4 points) (c) What is the prediction for the height of a child whose parents have an average height of 70.06 inches? (5 points)

Explanation / Answer

a) the intercept term equal to 19.6 gives the on an average height of the students without even considering the parental height.

And, the slope coefficient signify that as parental height increase/decrease by one unit, student height increase/decrease by 0.73 units.

b) R^2 gives the proportion of variation in dependent variable that is explained by the independent variables. Here, parental height explain only 45% of the variation in student height.

c) student height = 19.6 + 0.73(70.06) = 70.74

Thanks!

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