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 and 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 here:

level (%): 54 54 61 61 68

(mm): 16.473 18.693 14.305 15.121 13.505 level (%): 68 75 75 75

(mm): 11.640 11.168 12.534 11.224

(a) Calculate the least square estimates of the slope and intercept.

What is the estimate of Graph the regression model and the data.

2?

y  Deflection x  Stress y  Deflection x  Stress

(b) Find the estimate of the mean deflection if the stress level can be limited to 65%.

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

(d) To decrease the mean deflection by one millimeter, how much increase in stress level must be generated?

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