An article in Wood Science and Technology ("Creep in Chipboard, Part 3: Initial Assessment of the Influence of Moisture Content and Level of Stressing on Rate of Creep Time to Failure," Vol. 15, 1981, pp. 125-144) describes the results of a study of the deflection (mn of particleboard from stress levels of relative humidity. Assume that the two variables are related according to the simple linear regression model. The data are shown below: Stress level (%) Deflection (mm)

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An article in Wood Science and Technology ("Creep in Chipboard, Part 3: Initial Assessment of the Influence of Moisture Content and
Level of Stressing on Rate of Creep Time to Failure," Vol. 15, 1981, pp. 125-144) describes the results of a study of the deflection (mm)
of particleboard from stress levels of relative humidity. Assume that the two variables are related according to the simple linear
regression model. The data are shown below:
Štress level (%) Deflection (mm)
y
54
16.473
54
18.693
61
14.305
61
15.121
68
13.505
68
11.640
75
11.168
75
12.534
75
11.224
Minitab was used to fit a regression equation to the above data set. The results follow.
Predictor
Coef SE Coef
P
Constant
32.049
2.885 11.11 0.000
Stress level -0.27712 0.04361 -6.35 0.000
S= 1.05743, R-Sq = 85.2%, R-Sq(adj) = 83.1%
Analysis of Variance
Transcribed Image Text:An article in Wood Science and Technology ("Creep in Chipboard, Part 3: Initial Assessment of the Influence of Moisture Content and Level of Stressing on Rate of Creep Time to Failure," Vol. 15, 1981, pp. 125-144) describes the results of a study of the deflection (mm) of particleboard from stress levels of relative humidity. Assume that the two variables are related according to the simple linear regression model. The data are shown below: Štress level (%) Deflection (mm) y 54 16.473 54 18.693 61 14.305 61 15.121 68 13.505 68 11.640 75 11.168 75 12.534 75 11.224 Minitab was used to fit a regression equation to the above data set. The results follow. Predictor Coef SE Coef P Constant 32.049 2.885 11.11 0.000 Stress level -0.27712 0.04361 -6.35 0.000 S= 1.05743, R-Sq = 85.2%, R-Sq(adj) = 83.1% Analysis of Variance
Source
DF
MS
F P
Regression
1 45.154 45.154 40.38 0.000
Residual Error
7 7.827
1.118
Total
8 52.981
(a) Calculate the least square estimates of the slope and intercept. What is the estimate of o??
Round your answers to 3 decimal places.
i
,Bo =
i
(b) Find the estimate of the mean deflection if the stress level can be limited to 57%.
Round your answer to 2 decimal places.
i
(c) Estimate the change in the mean deflection associated with a 5% increment in stress level.
Round your answer to 2 decimal places.
(d) To decrease the mean deflection by 0.9 millimeters, how much increase in stress level must be generated?
Round your answer to 2 decimal places.
(e) Given that the stress level is 68%, find the fitted value of deflection and the corresponding residuals.
Round your answers to 2 decimal places.
Fitted value = i
Residuals (enter in ascending order of value): i
Transcribed Image Text:Source DF MS F P Regression 1 45.154 45.154 40.38 0.000 Residual Error 7 7.827 1.118 Total 8 52.981 (a) Calculate the least square estimates of the slope and intercept. What is the estimate of o?? Round your answers to 3 decimal places. i ,Bo = i (b) Find the estimate of the mean deflection if the stress level can be limited to 57%. Round your answer to 2 decimal places. i (c) Estimate the change in the mean deflection associated with a 5% increment in stress level. Round your answer to 2 decimal places. (d) To decrease the mean deflection by 0.9 millimeters, how much increase in stress level must be generated? Round your answer to 2 decimal places. (e) Given that the stress level is 68%, find the fitted value of deflection and the corresponding residuals. Round your answers to 2 decimal places. Fitted value = i Residuals (enter in ascending order of value): i
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