During oil drilling operations, components of the drilling assembly may suffer f

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 634 644 711 708 837 820 810 870 856 923 878 937 948 ?|100 92 87 84 77 75 74 63 57 55 47 43 38 ??.- ?.-892. ??.2 x8,741.668. ?7-65.864, y2 65,864, ???.-701.814 10.576. 8.741.668. (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 s. (Round your answer to four decimal places.) (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 appea r that this true average change has been precisely estimated? O This is a fairly narrow interval, soo has not been precisely estimated This is a fairly wide interval, so ?? has been precisely estimated. This is a fairly wide interval, so B, has not bean pracisaly astimated. O This is a fairly narrow interval, so, has been precisely estimated O This is a fairly wide interval, so B, has not been precisely estimated. You may need to use the appropriate table in the ??pendix of Tables to answer this question. Need Help?Read Tak to a Tutos

Explanation / Answer

SolutionA:

In excel isntall analysis tool packa nd then

data >data analysis >regression

SolutionA:

r sq=0.8876

solutionb:

standard erro of estiamte=

6.8985

Solutionc:

confidence inetrval for slope

this is a fairly narrow interval ,so Beta1 has been precisely estimated.

SUMMARY OUTPUT Regression Statistics Multiple R 0.942147 R Square 0.887642 Adjusted R Square 0.877427 Standard Error 6.898527 Observations 13 ANOVA df SS MS F Significance F Regression 1 4135.59 4135.59 86.901 1.48E-06 Residual 11 523.4865 47.58968 Total 12 4659.077 Coefficients Standard Error t Stat P-value Lower 95% Upper 95% Intercept 209.6102 15.24538 13.7491 2.84E-08 176.0554 243.1651 x -0.17331 0.018591 -9.32207 1.48E-06 -0.21423 -0.13239

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