Question

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

x i	1	2	3	4	5
y i	4	7	5	12	13

Round your answers to two decimal places.

A)

Using the following equation:

Estimate the standard deviation of ŷ* when x = 3.

B)

Using the following expression:

Develop a 95% confidence interval for the expected value of y when x = 3. _______to___________

C)  

Using the following equation:

Estimate the standard deviation of an individual value of y when x = 3.

D)

Using the following expression:

Develop a 95% prediction interval for y when x = 3. If your answer is negative, enter minus (-) sign. ________to_________

Answer 1

predicted val=1.3+6*2.3=

15.1000

SSE =Syy-(Sxy)2/Sxx=

13.900

	s2 =SSE/(n-2)=	4.6333
std error σ              =	=se =√s2=	2.1525

A)

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

0.96

B)

for 95 % CI value of t=		3.182
margin of error E=t*std error=		3.064
lower confidence bound=xo-E=		5.14
Upper confidence bound=xo+E=		11.26

95% confidence interval for the expected value =(5.14 , 11.26)

C)

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

2.36

D)

for 95 % CI value of t=		3.182
margin of error E=t*std error=		7.504
lower confidence bound=xo-E=		0.70
Upper confidence bound=xo+E=		15.70

95% prediction interval for y =(0.70 , 15.70)