The mean height of American women in their early twenties is about $64.5$ inches, with a standard deviation of about $2.7$ inches.
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If the correlation between the heights of married men and their wives is about $r = 0.5$, what is the equation of the regression line of the husband's height on the wife's height in young couples?
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Predict the height of the husband of a married woman who is $67$ inches tall.
I have tried on my own through reading and research to solve this problem but have been unable to come up with a solution because I do not know the standard deviation of the height of married men among these young couples nor their mean height. I need both to calculate the slope of the least-squares regression line and the $y$-intercept. Further, I have no dataset from which to calculate the mean or standard deviation of the height of young married men. Please help.
Best Answer
You haven't got enough information.
If the average height of married women is $64.5$ inches and the average height of married men is $69$ inches, then the line you're looking for would pass through the point $(64.5,\ 69).$ But that number $69$ (or whatever it is) is something you haven't got.
If the standard deviation of heights of wives is $2.7$ inches and the standard deviation of their husband's heights is $2.8$ inches and the correlation is $0.5$, then the slope of the line that predicts husbands' heights based on wive's heights is $0.5\times\dfrac{2.8}{2.7},$ but that number $2.8$ (or whatever is is) is something you haven't got.