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:

Given,

	x	y	(x-xbar)^2	(y-ybar)^2	(x-xbar)(y-ybar)
1	3	55	64	400	-150
2	12	40	1000	-25	5
3	6	55	25	400	-100
4	20	10	81	625	-225
5	14	15	9	400	-60
Total	55	175	180	1850	-540
Mean	11	35	SSX	SSY	SXY

Slope = -3.0000

Intercept = 68.0000

sample n = 5

SST = 1850

SSE = 230

SSR =1620

a)

Standard error of the confidence interval = s*sqrt(1 / n+(x - xbar)^2/Sxx)

substituting values & the we get

= 3.97

b)

Here for 95% confidence interval

alpha = 0.05

degree of freedom = 3

t(alpha/2 , df) = t(0.05/2 , 3) = 3.182

CI = x +/- t*standard error

substitute values & then we get

= (25.37 , 50.63)

c)

Standard error of prediction interval = s*sqrt(1 + 1/n+(x-xbar)^2/Sxx)

substitute values & then we get

= 9.61

d)

Now for 95 % confidence interval & -2 degree of freedom

Corresponding critical t value = 3.182

95% prediction interval = x +/- t*standard error

substitute values & then we get

= (7.41 , 68.59)