The article “Polyhedral Distortions in Tourmaline” (A.
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The article “Polyhedral Distortions in Tourmaline” (A. Ertl, J. Hughes, et al., The Canadian Mineralogist, 2002: 153–162) presents a model for calculating bond-length distortion in vanadium-bearing tourmaline. To check the accuracy of the model, several calculated values (x) were compared with directly observed values (y). The results (read from a graph) are presented in the following table.
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The article “Polyhedral Distortions in Tourmaline” (A.
1 answer below »
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Observed Value
Calculated Value
Observed Value
Calculated Value
0.33
0.36
0.74
0.78
0.36
0.36
0.79
0.86
0.54
0.58
0.97
0.97
0.56
0.64
1.03
1.11
0.66
0.64
1.10
1.06
0.66
0.67
1.13
1.08
0.74
0.58
1.14
1.17
a. Assume that the observed value y is an unbiased measurement of the true value. Show that if the calculated value x is accurate (i.e., equal to the true value), then y = x + ε, where ε is measurement error.
b. Compute the least-squares line y = + x.
c. Show that if the calculated value is accurate, then the true coefficients are β0 = 0 and β1 = 1.
d. Test the null hypotheses β0 = 0 and β1 = 1.
e. Is it plausible that the calculated value is accurate? Or can you conclude that it is not? Explain.
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