Question

11 point) Because elderly people may have difficulty standing to have their height measured, a study looked at the relationship between overall height and height to the knee. Here are data (in centimeters) for five elderly men: Knee Height x 56.9 44.2 40.6 44.8 55.7 Height y 190.3 155.3 146.1 164.9 170.9 Also, 2012 () = 3.61534688231022; What is the equation of the least-squares regression line for predicting height from knee height? ANSWER: ĝ=

Answer 1

Solution:

X	Y	XY	X^2	Y^2
56.9	190.3	10828.07	3237.61	36214.09
44.2	155.3	6864.26	1953.64	24118.09
40.6	146.1	5931.66	1648.36	21345.21
44.8	164.9	7387.52	2007.04	27192.01
55.7	170.9	9519.13	3102.49	29206.81

n	5
sum(XY)	40530.64
sum(X)	242.20
sum(Y)	827.50
sum(X^2)	11949.14
sum(Y^2)	138076.21
b	2.0581
a	65.8079

The equation of the regression line is

$\hat y$ = a + bx

The least -squares regression line for predicting height from knee height

Answer:  $\hat y$ = 65.8079 + 2.0581X