Question

We have a dataset with n= 10pairs of observations(xi,yi), and n∑i=1xi= 683,n∑i=1yi= 813,n∑i=1x2i= 47,405,n∑i=1xiyi= 56,089,n∑i=1y2i= 66,731.What is an approximate 99% confidence interval for the mean response atx0= 90?

Answer 1

Solution :

n=		10
Σx=		683
Σx2 =		47405
Σy =		813
Σy2 =		66731
Σxy=		56089
SSx=Σx2-(Σx)2/n=	756.1
SSy=Σy2-(Σy)2/n=	634.1
SP=Σxy-(ΣxΣy)/n=	561.1

b1= SP/Sxx =	0.7421
b=(Σy-bo*Σx)/n=	30.6147

SSE =Syy-(Sxy)2/Sxx=

217.71

	σ̂2=SSE/(n-2)=		27.21363
	σ̂=√σ̂2=			5.216668

from above:

n=	10
bo=	30.6147335
b1=	0.7421
sxy =√MSE=	5.2167
Sxx=(n-1)sx^2=	756.1
x̅ =	68.3

predcited value at X=90: =30.6147+90*0.7421 =

97.4035

std error confidence interval=	s*√(1/n+(x0-x̅)2/Sxx)	=	4.4351
for 99 % CI value of t=					3.3550
margin of error E=t*std error                            =			14.8796
lower confidence bound=sample mean-margin of error =		82.5239
Upper confidence bound=sample mean+margin of error=		112.2831

from above 99% CI =82.5239 , 112.2831

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