Question

Given are five observations for two variables, x and y.

xi	1	2	3	4	5
yi	3	8	6	11	13

Round your answers to two decimal places.

a. Using the following equation:

Estimate the standard deviation of ŷ* when x = 4.

b. Using the following expression:

Develop a 95% confidence interval for the expected value of y when x = 4.

to

c. Using the following equation:

Estimate the standard deviation of an individual value of y when x = 4.

d. Using the following expression:

Develop a 95% prediction interval for y when x = 4.

to

Answer 1

a)

std error of confidence interval =

s*√(1/n+(x0-x̅)2/Sxx)=

0.9950~ 0.99

b)

for 95 % confidence and 3degree of freedom critical t=		3.1820
95% confidence interval =xo -/+ t*standard error=	(7.33,13.67)

c)

std error of prediction interval=s*√(1+1/n+(x0-x̅)2/Sxx)=

2.0712~ 2.07

d)

for 95 % confidence and -2degree of freedom critical t=		3.1820
95% prediction interval =xo -/+ t*standard error=	(3.91,17.09)