Q. 1) The table below gives the readings from a laboratory experiment.3 5496 9Time (t)Reading (y) 721771161Fit:(i) a curve of the form y = ea(t-b) , and(ii)a curve of the form y = a(1 – bt )to the above data by method ofleast squares.-

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Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Civil engineers often use the straight-line equation, y = bo+b ₁x, to model the relationship between the shear strength y of masonry joints and precompression stress, x. To test this theory, a series of stress tests were performed on solid bricks arranged in triplets and joined with mortar. The precompression stress was varied for each triplet and the ultimate shear load just before failure (called the shear strength) was recorded. The stress results for n = 7 resulted in a Coefficient of Determination of 0.7589. Given that r ²= 0.7589, give a practical interpretation of r 2, the coefficient of determination for the least squares model. In repeated sampling, approximately 75.89% of all similarly constructed regression lines will accurately predict shear strength. We expect about 75.89% of the observed shear strength values to lie on the least squares line. We expect to predict the shear strength of a triplet test to within about 0.7589 tons of its true value. About 75.89% of the total…
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täble bel gives the reaaings from a la еxperimer Time (t) 2 3 5 6 9. Reading (y) 7 17 49 71 161 Fit: (i) a curve of the form y = ea(t-b) , and (ii)a curve of the form y = a(1 least squares. b' )to the above data by method of