The elastic limit^6 and ultimate strength^7of reinforcing steel^8 are often stat

Question

The elastic limit^6 and ultimate strength^7of reinforcing steel^8 are often stated to be a function of the bar size owing to differences in the rate of cooling when rolled. The data given in Table 3 were obtained by testing a random sample of the delivered reinforcing steel for a particular job. The "bar size" is given in terms of "bar number"9. The "bar number" equals the diameter of the bar in 1/8's of an inch. The "elastic limit" and "ultimate strength" are given in [psi]. The steel was classed as "intermediate grade" a. Are the elastic limit and ultimate strength correlated? Compute and report the correlation coefficient between the elastic limit and the ultimate strength. Plot the Elastic Limit (abscissa) versus the Ultimate Strength (ordinate). Does the data "look" correlated to your eye? b. The elastic limit may vary linearly with bar diameter or with the bar area^10. Carry out a regression analysis of the elastic limit as a function of the bar size. The elastic limit is the dependent variable the bar size is the independent variable. Compare and contrast the bar diameter and the bar area models. Which appears to be a better fit? Why do you think so? c. Repeat the previous analysis from part (b) using the ultimate strength data in lieu of the elastic limit data.

Explanation / Answer

a)

b)

As,Bar area is a function of bar diameter's square i used polynomial regression of order2. In the chart you can see the equation opf the regression line and R-square value. If R-square is higher than other model then we can say its a better model than another. So, here order 2 model is a better fit.

c)

Bar Size Elastic Limit Ultimate Strength 3 72830 95420 4 65120 89360 4 51930 81470 4 53299 77165 5 54400 73660 5 50690 78230 5 52219 78031 6 55450 79740 7 54250 83400 8 46500 73390 9 45690 71080 10 48300 76980 11 48470 78500 Corelation coefficient CORREL(B2:B14,C2:C14) 0.911541574 High corelation is there between elastic limit and ultimate strength, from the scatter plot also i see positive corelation between them.

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