# Least-Squares Regression Line from only the Mean and Standard Deviation of one Variable and the Correlation

The mean height of American women in their early twenties is about $64.5$ inches, with a standard deviation of about $2.7$ inches.

1. 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?

2. 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.

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.