Question

For the data set

(-1,-3), (3,3), (5,4), (9,8), (12,9)

find interval estimates (at a 92% significance level) for single values and for the mean value of y corresponding to x=8.

a) Interval Estimate for Single Value

b) Interval Estimate for Mean Value

Answer 1

point estimate for x=8 is y^ =0.9147*8-0.9225 =6.40

a)

std error of prediction interval=s*√(1+1/n+(x0-x̅)2/Sxx)=						1.3648
for 92 % confidence and -2degree of freedom critical t=						2.6050
92% prediction interval =xo -/+ t*standard error=					(2.8447 , 9.9553)

b)

std error of confidence interval =				s*√(1/n+(x0-x̅)2/Sxx)=		0.6160
for 92 % confidence and 3degree of freedom critical t=						2.6050
92% confidence interval =xo -/+ t*standard error=					(4.7954 , 8.0046)