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The following partial MINITAB regression output for the Fresh detergent data rel

ID: 3233555 • Letter: T

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


(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.)

(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.)


dv   =   


(d) For this case: n = 30, b0 = 8.388664, b1 = -.091904, and s = .587952. 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.)

Predicted Values for New Observations New Obs Fit SE Fit 95% CI 95% PI 1 8.3795 .1425 (8.0876, 8.6714) (7.1402, 9.6187) 2 8.3657 .108 (8.1444, 8.5869) (7.1412, 9.5902)

Explanation / Answer

Solution:

(a)

From the given table the point estimate is 8.3795

And a 95% confidence interval for the mean demand for fresh in all sales period when the price difference is 0.10 is [8.088, 8.671]

(b)

From the given table the point estimate is 8.3795

And a 95% prediction interval for the actual demand for fresh in all sales period when the price difference is 0.10 is [7.140, 9.619]

(c)

Calculate the distance value when x = 0.10. we have given that s = 0.587952 and sy = 0.1425 from the output

Distance value = (sy/s)2 = (0.1425/0.587952)2 = 0.0587

(d)

Calculate the 99% confidence interval and prediction interval x = 0.10 for the mean and lobor costs when:

We have given that n = 30, b0 = 8.388664, b1 = -0.091904, and s = .587952

Confidence Interval is:

= b0 + b1x

   = 8.388664 + (-0.091904) × 0.10 = 8.3794

= ± t/2 s(Distance value)

= 8.3794 ± 2.763(0.587952) 0.0587

= 8.3794 ± 0.39

= [8.7694, 7.9894]

This comparison (within rounding) to the computer generated output. For the prediction interval with the same quantities, we get:

± t/2 s(1 + Distance value)

8.3794 ± 2.763(0.587952) 1.0587

= 8.3794 ±1.67

= [10.0494, 6.7094]