Question

Given are five observations for two variables, x and y. (Round your answers to two decimal places.)

xi	3	12	6	20	14
yi	55	40	55	10	15

(a)

Estimate the standard deviation of

ŷ*

when

x = 10.

(b)

Develop a 95% confidence interval for the expected value of y when

x = 10.

to

(c)

Estimate the standard deviation of an individual value of y when

x = 10.

(d)

Develop a 95% prediction interval for y when

x = 10.

to

Answer 1

Answer:

	X	Y
1	3	55	64.0000	400.00	-150.0000
2	12	40	10000	-25.00	5.0000
3	6	55	25.0000	400.00	-100.0000
4	20	10	81.0000	625.00	-225.0000
5	14	15	9.0000	400.00	-60.0000
Total	55	175	180.0000	1850.00	-540.0000
Mean	11.000	35.000	SSX	SSY	SXY

Slope = -3.0000

Intercept = 68.0000

n = 5

SST = 1850.00

SSE = 230.00

SSR=1620.00

a)

std error of confidence interval = s*√(1/n+(x0-x̅)2/Sxx)= 3.9698~3.97
b)

for 95 % confidence and 3degree of freedom critical t= 3.1820
95% confidence interval =xo -/+ t*standard error= (25.37,50.63)
c)

std error of prediction interval=s*√(1+1/n+(x0-x̅)2/Sxx)= 9.6138~ 9.61
d)

for 95 % confidence and -2degree of freedom critical t= 3.1820
95% prediction interval =xo -/+ t*standard error= (7.41,68.59)