The article "Measurements of the Thermal Conductivity and Thermal Diffusivity of Polymer Melts with the Short-Hot-Wire Method" (X. Zhang, W. Hendro, et al., International Journal of Thermophysics, 2002:1077-1090) reports measurements of the thermal conductivity (in W· m-1 . K') and diffusivity of several polymers at several temperatures (in 1000°C). The following table presents results for the thermal conductivity of polycarbonate. Cond. Temp. 0.236 0.028 0.241 0.038 0.244 0.061 0.251 0.083 0.259 0.107 0.257 0.119 0.257 0.130 0.261 0.146 0.254 0.159 0.256 0.169 0.251 0.181 0.249 0.204 0.249 0.215 0.230 0.225 0.230 0.237 0.228 0.248 Denoting conductivity by y and temperature by x, fit the linear model y = Bo + Bix + ɛ. a. For each coefficient, test the hypothesis that the coefficient is equal to 0. b. Fit the quadratic model y = Bo + Bix + Bzx? + ɛ. For each coefficient, test the Page 661 Fit the cubic model y = Bo + Bix + Bx + Bax + ɛ. For each coefficient, test the %3D hypothesis that the coefficient is equal to 0. C. hypothesis that the coefficient is equal to 0. d. Fit the quartic model y = Bo + B1x + Bzx? + Bzx³ + Bx* + ɛ. For each coefficient, test the hypothesis that the coefficient is equal to 0. e. Which of the models in parts (a) through (d) is the most appropriate? Explain. f. Using the most appropriate model, estimate the conductivity at a temperature of 120°C.
The article "Measurements of the Thermal Conductivity and Thermal Diffusivity of Polymer Melts with the Short-Hot-Wire Method" (X. Zhang, W. Hendro, et al., International Journal of Thermophysics, 2002:1077-1090) reports measurements of the thermal conductivity (in W· m-1 . K') and diffusivity of several polymers at several temperatures (in 1000°C). The following table presents results for the thermal conductivity of polycarbonate. Cond. Temp. 0.236 0.028 0.241 0.038 0.244 0.061 0.251 0.083 0.259 0.107 0.257 0.119 0.257 0.130 0.261 0.146 0.254 0.159 0.256 0.169 0.251 0.181 0.249 0.204 0.249 0.215 0.230 0.225 0.230 0.237 0.228 0.248 Denoting conductivity by y and temperature by x, fit the linear model y = Bo + Bix + ɛ. a. For each coefficient, test the hypothesis that the coefficient is equal to 0. b. Fit the quadratic model y = Bo + Bix + Bzx? + ɛ. For each coefficient, test the Page 661 Fit the cubic model y = Bo + Bix + Bx + Bax + ɛ. For each coefficient, test the %3D hypothesis that the coefficient is equal to 0. C. hypothesis that the coefficient is equal to 0. d. Fit the quartic model y = Bo + B1x + Bzx? + Bzx³ + Bx* + ɛ. For each coefficient, test the hypothesis that the coefficient is equal to 0. e. Which of the models in parts (a) through (d) is the most appropriate? Explain. f. Using the most appropriate model, estimate the conductivity at a temperature of 120°C.
MATLAB: An Introduction with Applications
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ISBN:9781119256830
Author:Amos Gilat
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Chapter1: Starting With Matlab
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Transcribed Image Text:The article "Measurements of the Thermal Conductivity and Thermal Diffusivity of
Polymer Melts with the Short-Hot-Wire Method" (X. Zhang, W. Hendro, et al.,
International Journal of Thermophysics, 2002:1077-1090) reports measurements of the
thermal conductivity (in W· m-1 . K') and diffusivity of several polymers at several
temperatures (in 1000°C). The following table presents results for the thermal conductivity
of polycarbonate.
Cond.
Temp.
0.236
0.028
0.241
0.038
0.244
0.061
0.251
0.083
0.259
0.107
0.257
0.119
0.257
0.130
0.261
0.146
0.254
0.159
0.256
0.169
0.251
0.181
0.249
0.204
0.249
0.215
0.230
0.225
0.230
0.237
0.228
0.248
Denoting conductivity by y and temperature by x, fit the linear model y = Bo + Bix + ɛ.
a.
For each coefficient, test the hypothesis that the coefficient is equal to 0.
b. Fit the quadratic model y = Bo + Bix + Bzx? + ɛ. For each coefficient, test the
Page 661
Fit the cubic model y = Bo + Bix + Bx + Bax + ɛ. For each coefficient, test the
%3D
hypothesis that the coefficient is equal to 0.
C.
hypothesis that the coefficient is equal to 0.
d. Fit the quartic model y = Bo + B1x + Bzx? + Bzx³ + Bx* + ɛ. For each coefficient, test
the hypothesis that the coefficient is equal to 0.
e.
Which of the models in parts (a) through (d) is the most appropriate? Explain.
f.
Using the most appropriate model, estimate the conductivity at a temperature of 120°C.
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