Question

Short Answer Question We have a dataset with n - 10 pairs of observations (x, y), and 683, -813, -47,405, 1.4 - 56,089 - 66,731 What is an approximate 99% confidence interval for the mean response atto -90?

Answer 1

n=	10
Σx=	683
Σx2 =	47405
Σy =	813
Σy2 =	66731
Σxy=	56089
SSx=Σx2-(Σx)2/n=	756.1000
SSy=Σy2-(Σy)2/n=	634.1000
SP=Σxy-(ΣxΣy)/n=	561.1000

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

SSE =Syy-(Sxy)2/Sxx=

217.7090

σ̂2=SSE/(n-2)=	27.2136
σ̂=√σ̂2=	5.21667

predicted value at X=90 is:0.7421*90+30.6147=

97.404

standard error of CI=s*√(1/n+(x0-x̅)2/Sxx)=		4.4351
for 99 % CI value of t=		3.3550	(from excel:tinv(0.01,8)
margin of error E=t*std error=		14.8796
lower confidence bound=xo-E=		82.5239
Upper confidence bound=xo+E=		112.2831

95% confidence interval =(82.5239 , 112.2831)