Question

For the data set (−1,−1),(2,0),(6,5),(9,6),(12,11), find interval estimates (at a 95% significance level) for single values and for the mean value of ? corresponding to ?=1.

Note: For each part below, your answer should use interval notation.

Interval Estimate for Single Value =

Interval Estimate for Mean Value =

Answer 1

SSE =Syy-(Sxy)2/Sxx=

4.321

a	s2 =SSE/(n-2)=	1.4402
std error σ              =	=se =√s2=	1.2001

predicted val=-0.8974+1*0.9103=

0.013

a)

std error prediction interval= s*√(1+1/n+(x0-x̅)2/Sxx)=				1.4168
for 95 % CI value of t=				3.182
margin of error E=t*std error                            =				4.5088
lower prediction bound=sample mean-margin of error =				-4.4960
Upper prediction bound=sample mean+margin of error=				4.5217

Interval Estimate for Single Value = (-4.4960 , 4.5217)

b)

std error confidence interval= s*√(1/n+(x0-x̅)2/Sxx)=				0.7531
for 95 % CI value of t=				3.182
margin of error E=t*std error                            =				2.40
lower confidence bound=sample mean-margin of error =				-2.3838
Upper confidence bound=sample mean+margin of error=				2.4094

Interval Estimate for Mean Value = (-2.3838 , 2.4094)