Question

13.

(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     67.6 67.1 61.7 63.3 65.3 70.7 71 69.4 70.6 63.8 71 Sister 65.4 62.3 63.7 65.2 64.7 61.9 64.2 66.2 63.7 62.4 61.5 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 73 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

Solution =

X	Y	XY	X^2	Y^2
67.6	65.4	4421.04	4569.76	4277.16
67.1	62.3	4180.33	4502.41	3881.29
61.7	63.7	3930.29	3806.89	4057.69
63.3	65.2	4127.16	4006.89	4251.04
65.3	64.7	4224.91	4264.09	4186.09
70.7	61.9	4376.33	4998.49	3831.61
71	64.2	4558.2	5041	4121.64
69.4	66.2	4594.28	4816.36	4382.44
70.6	63.7	4497.22	4984.36	4057.69
63.8	62.4	3981.12	4070.44	3893.76
71	61.5	4366.5	5041	3782.25

  

n	11
sum(XY)	47257.38
sum(X)	741.50
sum(Y)	701.20
sum(X^2)	50101.69
sum(Y^2)	44722.66
Numerator	-108.62
Denominator	589.22
r	-0.1843
r square	0.0340
Xbar(mean)	67.4091
Ybar(mean)	63.7455
SD(X)	2.9472
SD(Y)	1.3646
b	-0.0838
a	69.3936

The value of the correlation,

r =  -0.184

The least-squares regression line,

= a + bx

=  69.39 +  -0.08x

=  69.39 + (-0.08)x