Problems 433
A designed experiment is run in the research and development laboratory, and the
following data, whereyis the time to failure in minutes, are obtained.yx 1 x 2 x 3
2,145 110 750 140
2,155 110 850 180
2,220 110 1,000 140
2,225 110 1,100 180
2,260 120 750 140
2,266 120 850 180
2,334 120 1,000 140
2,340 130 1,000 180
2,212 115 840 150
2,180 115 880 150(a) Fit a multiple regression model to these data.
(b) Estimate the error variance.
(c) Determine a 95 percent confidence interval for the mean time to failure
when the operating voltage is 125, the motor speed is 900, and the operating
temperature is 160.
50.Explain why, for the same data, a prediction interval for a future response always
contains the corresponding confidence interval for the mean response.
51.Consider the following data set.x 1 x 2 y
5.1 2 55.42
5.4 8 100.21
5.9 − 2 27.07
6.6 12 169.95
7.5 − 6 −17.93
8.6 16 197.77
9.9 − 10 −25.66
11.4 20 264.18
13.1 − 14 −53.88
15 24 317.84
17.1 − 18 −72.53
19.4 28 385.53(a) Fit a linear relationship betweenyandx 1 ,x 2.
(b) Determine the variance of the error term.