Stat 13 lecture 23 correlation and regression A cartoon from handout The taller the father, the taller the son Tall father’s son is taller than short farther’s.

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Stat 13 lecture 23 correlation and regression A cartoon from handout The taller the father, the taller the son Tall father’s son is taller than short farther’s son But tall father’s son is not as tall as father; short father’s son is not as short as father Galton’s data

Regression line The formula : y=  y +r[SD(Y)/SD(X)](x-  x ) where  y is mean of Y and  x is mean of X Application : (a) predict IQ at age 35 for someone with IQ of 110 at age 18. (b) predict IQ at age 35 for someone with IQ 90 of at age 18

Answer (a) y= (15/15) ( ) =108, Observe that this is greater than average but less than x=110 (b) y= (15/15) (90-100)=92, This is smaller than average but is greater than x=90. This is consistent with the cartoon.

SD line is the ideal that data will line up when r=1, perfect correlation situation Regression line is the line of prediction ; because r is typically less than 1, it is not as steep as SD line Y X (inverse)Regr ession line for predicting X Slope of SD line = SD(Y)/SD(X) Slope of regression line = r [SD(Y)/SD(X)]