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:
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
Minitab was used to fit a regression equation to the above dataset. The results follow.
(a) Calculate the least square estimates of the slope and intercept. What is the estimate ofσ2?
(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.