Please answer exercises 11.2.7 and 11.2.8 Stepwise

a. Calculate the least square estimates of the slope and inter- cept. What is the estimate of o*? 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 1n stress level must be generated? e. Given that the stress level is 68%, find the fitted value of deflection and the corresponding residual. _. =. zm i = = a = 11.2.7 (URRY GSB An article in the Journal of the American Ceramic Society [\"Rapid Hot-Pressing of Ultrafine PSZ Powders\" (1991, Vol. 74, pp. 15471553)] considered the microstructure of the ultrafine powder of partially stabilized zir- conia as a function of temperature. The data follow: x = Temperature (C): 1100 1200 1300 1100 1500 1200 = 1300 y = Porosity (%): 30.8 19.2 6.0 13.5 11.4 do 3.6 a. Fit the simple linear regression model using the method of least squares. Find an estimate of 07. b. Estimate the mean porosity for a temperature of 1400 C. c. Find the fitted value corresponding to y = 11.4 and the associated residual. d. Draw a scatter diagram of the data. Does a simple linear regression model seem appropriate here? Explain. 11.2.8 An article in Wood Science and Technology |\"Creep in Chipboard, Part 3: Initial Assessment of the Influence of Mois- ture 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: x = Stress level (%): 54 54 61 61 68 y = Deflection (mm): 16.473 18.693 14.305 15.121 13.505 x = Stress level (%): 68 75 TS 75 y = Deflection (mm): 11.640 11.168 12.534 11.224