An article in Wood Science and Technology (“Creepin Chipboard, Part 3: Initial A

Question

An article in Wood Science and Technology (“Creepin Chipboard, Part 3: Initial Assessment of the Influence ofMoisture Content and Level of Stressing on Rate of Creep Time toFailure,” Vol. 15, 1981, pp. 125-144) describes the resultsof a study of the deflection (mm) of particleboard from stresslevels of relative humidity. Assume that the two variables arerelated according to the simple linear regression model. The dataare shown below:

Minitab was used to fit a regression equation to the above dataset. The results follow.

(a) Calculate the least square estimates of theslope and intercept. What is the estimate of2?

(b) Find the estimate of the mean deflection ifthe stress level can be limited to 69%.

(c) Estimate the change in the mean deflectionassociated with a 5% increment in stress level.

(d)To decrease the mean deflection by 1.2millimeters, how much increase in stress level must begenerated?

(e)Given that the stress level is 68%, find thefitted value of deflection and the corresponding residuals.

fitted value =
residuals (enter in ascending order of value): ,

Stress level (%)
x 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 An article in Wood Science and Technology (^''Creepin Chipboard, Part 3: Initial Assessment of the Influence ofMoisture Content and Level of Stressing on Rate of Creep Time toFailure,^'' Vol. 15, 1981, pp. 125-144) describes the resultsof a study of the deflection (mm) of particleboard from stresslevels of relative humidity. Assume that the two variables arerelated according to the simple linear regression model. The dataare shown below: Minitab was used to fit a regression equation to the above dataset. The results follow. (a) Calculate the least square estimates of theslope and intercept. What is the estimate of sigma^2? (b) Find the estimate of the mean deflection ifthe stress level can be limited to 69%. (c) Estimate the change in the mean deflectionassociated with a 5% increment in stress level. (d)To decrease the mean deflection by 1.2millimeters, how much increase in stress level must begenerated? (e)Given that the stress level is 68%, find thefitted value of deflection and the corresponding residuals. fitted value = residuals (enter in ascending order of value):

Explanation / Answer

(b) Find the estimate of the mean deflection ifthe stress level can be limited to 69%.

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