An article in the Journal of the American Ceramic Society [Rapid Hot-Pressing of Ultrafi ne PSZ Powders

An article in the Journal of the American Ceramic Society [€œRapid Hot-Pressing of Ultrafi ne PSZ Powders€ (1991, Vol. 74, pp. 1547€“1553)] considered the microstructure of the ultrafi ne powder of partially stabilized zirconia as a function of temperature. The data follow:

TABLE 11-4 Propellant Data

(a) Fit the simple linear regression model using the method of least squares. Find an estimate of σ².

(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.

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x= Temperature (°C): 1100 1200 1300 1100 1500 1200 1300 y = Porosity (%): 30.8 19.2 6.0 13.5 11.4 3.6 7.7 Strength y (psi) Observation Age x (weeks) Number 2158.70 15.50 1678.15 23.75 3 2316.00 8.00 4 2061.30 17.00 2207.50 5.000 1708.30 19.00 1784.70 24.00 8. 2575.00 2.50 2357.90 7.50 10 2277.70 11.00 11 2165.20 13.00 12 2399.55 3.75 13 1779.80 25.00 14 2336.75 9.75 15 1765.30 22.00 16 2053.50 18.00 17 2414.40 6.00 18 2200.50 12.50 19 2654.20 2.00 20 1753.70 21.50