Question

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. If the correlation between the heights of husbands and wives is about r = 0.5, what is the slope of the regression line used to predict the husband's height (Y) from the wife's height (X) in young couples?

Answer 1

Answer:

slope= 0.52

Step-by-step explanation:

For American women

Mean (x) = 64 inches

Standard deviation (sx) = 2.7 inches

For American Men

Mean(ÿ) = 69.3 inches

Standard deviation (sy) = 2.8 inches

r = 0.5

Slope = ??

Husband height = Y

Wife height = X

the general equation of regression line

y = a + bx

The slope of the regression line is the linear correlation coefficient multiplied by the standard deviation for Y

b = r (sy/sx)

b = 0.5(2.8/2.7)

b = 0.52

The intercept a = ÿ - bx

a = 69.3 - 0.52(64)

a = 69.3 - 33.28

a = 36.02

The equation of the regression line y = a + bx

y = 36.02 + 0.52x