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The article "Polyhedral Distortions in Tourmaline" (A. Eril, 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. Observed Value Calculated Value 0.33 0.36 0.36 0.36 0.54 0.58 0.56 0.66 0.64 0.64 0.66 0.67 0.74 0.58 0.74 0.78 0.79 0.86 0.97 0.97 1.11 1.03 110 1.06 1.13 1.08 114 117 Assume that the observed value y is an unbiased measurement of the true value. Show that if the calculated value x is accurate (ie., equal to the true value), then y = x+ , where e is measurement error. a. b. Compute the least-squares line y= Show that if the calculated value is accurate, then the true coefficients are , = Oand e, Â, + Â,x- C. =1. d. Test the null hypotheses e,-0 and e, = 1. Is it plausible that the calculated value is accurate? Or can you conclude that it is not? Explain. e.

The article "Polyhedral Distortions in Tourmaline" (A. Eril, 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. Observed Value Calculated Value 0.33 0.36 0.36 0.36 0.54 0.58 0.56 0.66 0.64 0.64 0.66 0.67 0.74 0.58 0.74 0.78 0.79 0.86 0.97 0.97 1.11 1.03 110 1.06 1.13 1.08 114 117 Assume that the observed value y is an unbiased measurement of the true value. Show that if the calculated value x is accurate (ie., equal to the true value), then y = x+ , where e is measurement error. a. b. Compute the least-squares line y= Show that if the calculated value is accurate, then the true coefficients are , = Oand e, Â, + Â,x- C. =1. d. Test the null hypotheses e,-0 and e, = 1. Is it plausible that the calculated value is accurate? Or can you conclude that it is not? Explain. e.

MATLAB: An Introduction with Applications
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
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The article "Polyhedral Distortions in Tourmaline" (A. Eril, 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. Observed Value Calculated Value 0.33 0.36 0.36 0.36 0.54 0.58 0.56 0.66 0.64 0.64 0.66 0.67 0.74 0.58 0.74 0.78 0.79 0.86 0.97 0.97 1.11 1.03 110 1.06 1.13 1.08 114 117 Assume that the observed value y is an unbiased measurement of the true value. Show that if the calculated value x is accurate (ie., equal to the true value), then y = x+ , where e is measurement error. a. b. Compute the least-squares line y= Show that if the calculated value is accurate, then the true coefficients are , = Oand e, Â, + Â,x- C. =1. d. Test the null hypotheses e,-0 and e, = 1. Is it plausible that the calculated value is accurate? Or can you conclude that it is not? Explain. e.
Transcribed Image Text:The article "Polyhedral Distortions in Tourmaline" (A. Eril, 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. Observed Value Calculated Value 0.33 0.36 0.36 0.36 0.54 0.58 0.56 0.66 0.64 0.64 0.66 0.67 0.74 0.58 0.74 0.78 0.79 0.86 0.97 0.97 1.11 1.03 110 1.06 1.13 1.08 114 117 Assume that the observed value y is an unbiased measurement of the true value. Show that if the calculated value x is accurate (ie., equal to the true value), then y = x+ , where e is measurement error. a. b. Compute the least-squares line y= Show that if the calculated value is accurate, then the true coefficients are , = Oand e, Â, + Â,x- C. =1. d. Test the null hypotheses e,-0 and e, = 1. Is it plausible that the calculated value is accurate? Or can you conclude that it is not? Explain. e.
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