Question

(5.37) How strongly do physical characteristics of sisters and brothers correlate? Here are data on the heights (in inches) of 11 adult pairs (Use a statistics technology and not the rounded regression equation to solve the problems):

Brother 65.2 64.1 70.2 67.4 65.8 68.4 72.5 71.2 67.7 66.6 62.2

Sister 71.9 60.9 69.6 63 61.2 59.1 69.8 63.4 70.6 56 66.7

What is the value of the correlation rounded to at least three decimal places? r = ___

What is the equation of the least-squares regression line for predicting a sister's height from her brother's height? (Round the coefficients to at least two decimal places.)

yˆ= ___ + ___x

If Damien is 66.3 inches tall, predict the height (± 0.1 inch) of his sister Tonya: height = ___ inches.

What percent of the variation in the sisters' height among these subjects is explained by the straight-line relationship with the brother's height? (Give your answer as a whole number.) ___%

Answer 1

Now,

Tonya height = 43.666 + 0.3128*66.3 = 64.4 inches

Percent of the variation in the sisters' height among these subjects is explained by the straight-line relationship with the brother's height = r² = 0.183² = 3 %