Question

The mean height of married American women in their early twenties is 64.5 inches and the standard deviation is 2.5 inches. The mean height of married mean the same age is 68.5 inches, with standard deviation of 2.7 inches. The correlation between the heights of husbands and wives is about r = 0.5. a) Find the equation of the least-squares regression line for predicting a husband’s height from the wife’s height for married couples in their early 20s.

Answer 1

Answer:

The equation for regression line and predicting a husband's height for married couples in their early 20s

Equation: Y'=33.67+0.54*X'

Step-by-step explanation:

r=0.5

x'=64.5

Sx=2.5

y'=68.5

Sy=2.7

General regression line equation is:

Y'=a+b*X'

so the slope of the regression line is the linear correlation coefficient multiplied by the standard deviation for y' divided by the standard deviation for x'

$b=r*\frac{S_{y}}{S_{x}}\\b=0.5*\frac{2.7}{2.5}\\b=0.54$

The intercept with axis y is the mean of the decreased by the product of the slope and the mean of x

$a=y'-b*x'\\a=68.5-0.54*64.5\\a=33.67$

The equation regression line then is:

Y'=33.67+0.54*X'