The mean height of American women in their twenties is about 64 inches, and the standard
deviation is about 2.7 inches. The mean height of men the same age is about 69.3 inches with
standard deviation about 2.8 inches. Suppose correlation between the heights of husbands and
wives is about r =0.5. What is the intercept of the least squares regression line?
deviation is about 2.7 inches. The mean height of men the same age is about 69.3 inches with
standard deviation about 2.8 inches. Suppose correlation between the heights of husbands and
wives is about r =0.5. What is the intercept of the least squares regression line?
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If x=women and y=men
I'm not sure if you are familiar with the formulas below
The slope b is given by
b=r*sy/sx sx is SD for women and sy is SD for men
b=(0.5)(2.8)/(2.7)=0.519
The intercept a is given by
a=ybar-b*xbar
=69.3-(0.519)(64)
=69.3-33.2=36.1
Then
y'=36.1 + 0.519x
I'm not sure if you are familiar with the formulas below
The slope b is given by
b=r*sy/sx sx is SD for women and sy is SD for men
b=(0.5)(2.8)/(2.7)=0.519
The intercept a is given by
a=ybar-b*xbar
=69.3-(0.519)(64)
=69.3-33.2=36.1
Then
y'=36.1 + 0.519x