An article in the Journal of the American Ceramic Society, "Rapid Hot-Pressing of Ultrafine PSZ Powders" (1991, Vol. 74, pp. 1547-1553) considered the microstructure of the ultrafine powder of partially stabilized zirconia as a function of temperature. The data are shown below: x = Temperature (°C) 1100 1200 1300 1100 1500 1200 1300 30.8 19.2 6 13.5 11.4 7.7 3.6 y = Porosity (%) (a) Fit the simple linear regression model using the method of least squares. Find the least squares estimates of the intercept and slope in the simple linear regression model. Find an estimate of o².

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter7: Analytic Trigonometry
Section7.6: The Inverse Trigonometric Functions
Problem 91E
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An article in the Journal of the American Ceramic Society, "Rapid Hot-Pressing of Ultrafine PSZ Powders" (1991, Vol. 74, pp. 1547-1553)
considered the microstructure of the ultrafine powder of partially stabilized zirconia as a function of temperature. The data are shown
below:
x = Temperature (°C) 1100 1200 1300 1100 1500 1200 1300
30.8 19.2 6
13.5 11.4 7.7 3.6
y = Porosity (%)
(a) Fit the simple linear regression model using the method of least squares. Find the least squares estimates of the intercept and slope
in the simple linear regression model. Find an estimate of o².
Bo
= i
(Round your answer to 3 decimal places.)
= i
(Round your answer to 5 decimal places.)
= i
(Round your answer to 2 decimal places.)
(b) Estimate the mean porosity for a temperature of 1368 °C.
y
= i
(Round your answer to 2 decimal places.)
65
a>
Transcribed Image Text:An article in the Journal of the American Ceramic Society, "Rapid Hot-Pressing of Ultrafine PSZ Powders" (1991, Vol. 74, pp. 1547-1553) considered the microstructure of the ultrafine powder of partially stabilized zirconia as a function of temperature. The data are shown below: x = Temperature (°C) 1100 1200 1300 1100 1500 1200 1300 30.8 19.2 6 13.5 11.4 7.7 3.6 y = Porosity (%) (a) Fit the simple linear regression model using the method of least squares. Find the least squares estimates of the intercept and slope in the simple linear regression model. Find an estimate of o². Bo = i (Round your answer to 3 decimal places.) = i (Round your answer to 5 decimal places.) = i (Round your answer to 2 decimal places.) (b) Estimate the mean porosity for a temperature of 1368 °C. y = i (Round your answer to 2 decimal places.) 65 a>
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