Question

The following partial MINITAB regression output for the Fresh detergent data relates to predicting demand for future sales periods in which the price difference will be .10

Predicted Values for New Observations
New	Obs	Fit	SE Fit	95% CI	95% PI
	1	8.3323	.1570	(8.0107, 8.6539)	(6.7456, 9.9189)
	2	8.3601	.142	(8.0689, 8.6512)	(6.7793, 9.9408)

(a) Report a point estimate of and a 95 percent confidence interval for the mean demand for Fresh in all sales periods when the price difference is .10. (Round your answers to 3 decimal places.)

Point estimate =

Confidence interval = [, ]

(b) Report a point prediction of and a 95 percent prediction interval for the actual demand for Fresh in an individual sales period when the price difference is .10. (Round your answers to 3 decimal places.)

Point estimate =

Confidence interval = [, ]

(c) Remembering that s = .758487 and that the distance value equals (syˆ/s)2(sy^/s)2, use syˆsy^_· from the computer output to hand calculate the distance value when x = .10. (Round your answer to 4 decimal places.)

dv   =   

(d) For this case: n = 30, b₀ = 8.313738, b₁ = .185319, and s = .758487. Using this information, and your result from part (c), find 99 percent confidence and prediction intervals for mean and individual demands when x = .10. (Round your answers to 4 decimal places.)

99% C.I.:[, ]

99% P.I.:[, ]

Answer 1

a)

Point estimate =8.3323

Confidence interval =(8.0107 , 8.6539)

b)

Point estimate =8.3323

Confidence interval =(6.7456 , 9.9189)

c)

distance value(leverage) =(sy/s)^2 =

0.0428

d)

std error confidence interval=		s*√(leveage)		=	0.1570
for 99 % CI value of t=					2.7633
margin of error E=t*std error                            =					0.43
lower confidence bound=sample mean-margin of error =					7.8984
Upper confidence bound=sample mean+margin of error=					8.7661

99% CI =7.8984 , 8.7661

std error prediction interval=		s*√(1+leverage)		=	0.7746
for 99 % CI value of t=					2.7633
margin of error E=t*std error                            =					2.14
lower prediction bound=sample mean-margin of error =					6.1919
Upper prediction bound=sample mean+margin of error=					10.4726

99% PI =6.1919 , 10.4726