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During oil drilling operations, components of the drilling assembly may suffer from sulfide stress cracking. An article reported on a study in which the composition of a standard grade of steel was analyzed. The following data on y = threshold stress (% SMYS) and x = yield strength (MPa) was read from a graph in the article (which also included the equation of the least squares line). x 634 645 712 707 835 820 810 870 856 923 878 937 948 y 100 92 89 83 76 75 74 63 57 55 47 43 38 2 Σχ. – 10,575, Σ.Υ. – 892, Σx - 8,739,621, Σy - 65,896, Σχ – 701,637 (a) What proportion of observed variation in stress can be attributed to the approximate linear relationship between the two variables? (Round your answer to four decimal places.) (b) Compute the estimated standard deviation sa, (Round your answer to four decimal places.) 1 501 (c) Calculate a confidence interval using confidence level 95% for the expected change in stress associated with a 1 MPa increase in strength. (Round your answers to three decimal places.) Does it appear that this true average change has been precisely estimated? This is a fairly wide interval, so has been precisely estimated. This is a fairly narrow interval, so ß, has been precisely estimated. O This is a fairly wide interval, so , has been precisely estimated. This is a fairly wide interval, so , has not been precisely estimated. O This is a fairly narrow interval, so o has not been precisely estimated. You may need to use the appropriate table in the Appendix of Tables to answer this question.

During oil drilling operations, components of the drilling assembly may suffer from sulfide stress cracking. An article reported on a study in which the composition of a standard grade of steel was analyzed. The following data on y = threshold stress (% SMYS) and x = yield strength (MPa) was read from a graph in the article (which also included the equation of the least squares line). x 634 645 712 707 835 820 810 870 856 923 878 937 948 y 100 92 89 83 76 75 74 63 57 55 47 43 38 2 Σχ. – 10,575, Σ.Υ. – 892, Σx - 8,739,621, Σy - 65,896, Σχ – 701,637 (a) What proportion of observed variation in stress can be attributed to the approximate linear relationship between the two variables? (Round your answer to four decimal places.) (b) Compute the estimated standard deviation sa, (Round your answer to four decimal places.) 1 501 (c) Calculate a confidence interval using confidence level 95% for the expected change in stress associated with a 1 MPa increase in strength. (Round your answers to three decimal places.) Does it appear that this true average change has been precisely estimated? This is a fairly wide interval, so has been precisely estimated. This is a fairly narrow interval, so ß, has been precisely estimated. O This is a fairly wide interval, so , has been precisely estimated. This is a fairly wide interval, so , has not been precisely estimated. O This is a fairly narrow interval, so o has not been precisely estimated. You may need to use the appropriate table in the Appendix of Tables to answer this question.

Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN:9781285463247
Author:David Poole
Publisher:David Poole
Chapter7: Distance And Approximation
Section7.3: Least Squares Approximation
Problem 34EQ
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During oil drilling operations, components of the drilling assembly may suffer from sulfide stress cracking. An article reported on a study in which the composition of a standard grade of steel was analyzed. The following data on y = threshold stress (% SMYS) and x = yield strength (MPa) was read from a graph in the article (which also included the equation of the least squares line). x 634 645 712 707 835 820 810 у 100 76 75 Σ×, = 10,575, Σy, = 892, Σx = 8,739,621, Σy = 65,896, Σχιν, = 701,637 (a) What proportion of observed variation in stress can be attributed to the approximate linear relationship between the two variables? (Round your answer to four decimal places.) 92 89 83 74 870 856 923 878 937 63 57 55 47 43 Does it appear that this true average change has been precisely estimated? O This is a fairly wide interval, so has been precisely estimated. O This is a fairly narrow interval, so ß, has been precisely estimated. O This is a fairly wide interval, so, has been precisely estimated. O This is a fairly wide interval, so ß, has not been precisely estimated. O This is a fairly narrow interval, so ßo has not been precisely estimated. 948 (b) Compute the estimated standard deviation $₁(Round your answer to four decimal places.) 581 (c) Calculate a confidence interval using confidence level 95% for the expected change in stress associated with a 1 MPa increase in strength. (Round your answers to three decimal places.) You may need to use the appropriate table in the Appendix of Tables to answer this question. 38
Transcribed Image Text:During oil drilling operations, components of the drilling assembly may suffer from sulfide stress cracking. An article reported on a study in which the composition of a standard grade of steel was analyzed. The following data on y = threshold stress (% SMYS) and x = yield strength (MPa) was read from a graph in the article (which also included the equation of the least squares line). x 634 645 712 707 835 820 810 у 100 76 75 Σ×, = 10,575, Σy, = 892, Σx = 8,739,621, Σy = 65,896, Σχιν, = 701,637 (a) What proportion of observed variation in stress can be attributed to the approximate linear relationship between the two variables? (Round your answer to four decimal places.) 92 89 83 74 870 856 923 878 937 63 57 55 47 43 Does it appear that this true average change has been precisely estimated? O This is a fairly wide interval, so has been precisely estimated. O This is a fairly narrow interval, so ß, has been precisely estimated. O This is a fairly wide interval, so, has been precisely estimated. O This is a fairly wide interval, so ß, has not been precisely estimated. O This is a fairly narrow interval, so ßo has not been precisely estimated. 948 (b) Compute the estimated standard deviation $₁(Round your answer to four decimal places.) 581 (c) Calculate a confidence interval using confidence level 95% for the expected change in stress associated with a 1 MPa increase in strength. (Round your answers to three decimal places.) You may need to use the appropriate table in the Appendix of Tables to answer this question. 38
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