An article in Wood Science and Technology [Creep in Chipboard, Part 3: Initial Assessment of the Influence

An article in Wood Science and Technology [€œCreep in Chipboard, Part 3: Initial Assessment of the Influence of Moisture Content and Level of Stressing on Rate of Creep and Time to Failure€ (1981, Vol. 15, pp. 125€“144)] reported 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 follow:

(a) Calculate the least square estimates of the slope and intercept. What is the estimate of σ2? Graph the regression model and the data.

(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.

Transcribed Image Text:

x= Stress level (%): y = Deflection (mm): x= Stress level (%): y = Deflection (mm): 54 54 61 61 68 16.473 18.693 14.305 15.121 13.505 75 75 75 11.640 11.168 12.534 11.224 68