Question

Chapter 2, Section 5, Exercise 176 Use StatKey or other technology to find the correlation for the following data.

X35276 Y232.553.45 Click here to access Statkey. Round your answer to three decimal places. The correlation is r- the absolute tolerance is +/-0.001

Chapter 2, Section 6, Exercise 200

Two variables are defined, a regression equation is given, and one data point is given.

	Hgt	=	height in inches
	Age	=	age in years of a child
	Hgt^	=	23.8+2.71(Age)

The data point is a child 12 years old who is 60 inches tall.

YES OR NO?

Answer 1

176)

X	Y	(x-x̅)²	(y-ȳ)²	(x-x̅)(y-ȳ)
3	2	2.56	1.4	1.9
5	3	0.16	0.0	-0.1
2	2.5	6.76	0.5	1.8
7	5	5.76	3.2	4.3
6	3.5	1.96	0.1	0.4

	ΣX	ΣY	Σ(x-x̅)²	Σ(y-ȳ)²	Σ(x-x̅)(y-ȳ)
total sum	23	16	17.200	5.3	8.4
mean	4.60	3.20	SSxx	SSyy	SSxy

sample size ,   n =   5          
here, x̅ =   4.60   ,   ȳ =   3.2  
                  
SSxx =    Σ(x-x̅)² =    17.20          
SSxy=   Σ(x-x̅)(y-ȳ) =   8.4          

correlation coefficient ,    r = Sxy/√(Sx.Sy) = 8.4/√(17.20*5.3) = 0.880

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200)

Hgt^=23.8+2.71(Age)

x=12

a)

so, predicted value

Hgt^=23.8+2.71*12= 56.32 inches

residual = actual -predicted value = 60 - 56.32 =3.68inches

b)

given one year increase in age, expected change in height is 2.71

c)

if age is 0, the predicted height will be =23.8 inches

that tis does not make any sense

so, answer is NO