# Regression question from Freedman Statistics

From Freedmans statistics, page 165, Regression, Exercise Set D.

Question :

Answer : "Well under 50% - the regression effect"

I'm not sure about the reasoning for this though, I'm not sure I really follow what the question is asking either.

They haven't said that there's any relation or whatever between education and income for this question, though the way it's setup I'm thinking that they're assuming something like this :

I'm told that we're referring to people in the 90th percentile of education, so that would be the blue part of this graph (?) :

I'm not sure how to reason about income based on this, with respect to the education level and this question .

I'm not sure if the graphs that I've provided are helpful or not either.

• They're definitely assuming some relationship (it wouldn't make sense to talk about the regression effect otherwise), and there's certainly a relationship in practice. Are you sure there was no relationship discussed earlier in the chapter? You may like to look at this drawing by Galton; the numbers are counts in cells, and the ellipse represents a contour of the joint distribution of parental average height (sort of) and ... ctd – Glen_b Nov 19 '17 at 22:43
• ctd... child adult height (again sort of -- females are multiplied by 1.08). The regression lines of y on x and x on y are those "tangent lines"; in each case the conditional mean of the response at any given number of standard deviations from the mean for the predictor is closer to the overall reponse-mean (this is "regression to the mean" and it's where the word "regression" in linear regression comes from). The "major axis" line is the line marking equal numbers of standard deviations from the mean on both variables. – Glen_b Nov 20 '17 at 0:43
• Of course neither education nor income will be very close to normally distributed (neither the marginal nor the conditional distributions) but the basic notion of a tendency to see regression to the mean still carries over. – Glen_b Nov 20 '17 at 0:46